تكلم مع الذكاء الاصطناعي
Deck 3: Applications of Differentiation
ملء الشاشة (f)
سؤال
Find the most general antiderivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find f.
سؤال
A particle moves along a straight line with velocity function 
and its initial displacement is 
. Find its position function.
and its initial displacement is . Find its position function. سؤال
A company estimates that the marginal cost (in dollars per item) of producing items is 
. If the cost of producing one item is $560 find the cost of producing 400 items.
. If the cost of producing one item is $560 find the cost of producing 400 items. سؤال
Find the most general antiderivative of the function. 
سؤال
Find the most general antiderivative of the function. 
سؤال
A ballast is dropped from a stationary hot-air balloon that is at an altitude of 256 ft. Find (a) an expression for the altitude of the ballast after t seconds, (b) the time when it strikes the ground, and (c) its velocity when it strikes the ground. (Disregard air resistance and take 
.)
.) سؤال
سؤال
A car braked with a constant deceleration of 
, producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?
, producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied? سؤال
سؤال
Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at 
is 
, find f (1) .
A)11
B)1
C)0
D)12
E)6
is , find f (1) .A)11
B)1
C)0
D)12
E)6
سؤال
Estimate the value of 
by using three iterations of Newton's method to solve the equation 
with initial estimate 
Round your final estimate to four decimal places.
A)1.71
B)2.2662
C)2.2361
D)1.6535
by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.A)1.71
B)2.2662
C)2.2361
D)1.6535
سؤال
Suppose the line 
is tangent to the curve 
when 
. If Newton's method is used to locate a root of the equation 
and the initial approximation is 
, find the second approximation 
.
is tangent to the curve when . If Newton's method is used to locate a root of the equation and the initial approximation is , find the second approximation . سؤال
Evaluate 
, and tell whether its antiderivative F is increasing or decreasing at the point 
radians.
A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
, and tell whether its antiderivative F is increasing or decreasing at the point radians.A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
سؤال
Use Newton's method to approximate the zero of 
between 
and 
using 
. Continue until two successive approximations differ by less than 0.00001.
A)0.16904
B)0.11154
C)0.23624
D)0.07984
between and using . Continue until two successive approximations differ by less than 0.00001.A)0.16904
B)0.11154
C)0.23624
D)0.07984
سؤال
Use Newton's method to approximate the indicated root of 
in the interval 
, correct to six decimal places.
Use
as the initial approximation.
in the interval , correct to six decimal places.Use
as the initial approximation. سؤال
The size of the monthly repayment k that amortizes a loan of A dollars in N years at an interest rate of r per year, compounded monthly, on the unpaid balance is given by 
The value of r can be found by performing the iteration 
A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.
A)8.7%
B)7.7%
C)6.7%
D)5.7%
The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.A)8.7%
B)7.7%
C)6.7%
D)5.7%
سؤال
Find the position function of a particle moving along a coordinate line that satisfies the given condition. 
, s(1) = -1
, s(1) = -1 سؤال
Use Newton's method with the specified initial approximation 
to find 
, the third approximation to the root of the given equation. (Give your answer to four decimal places.) 
to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.) سؤال
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. 
, s(0) = 5, v(0) = 0
, s(0) = 5, v(0) = 0 سؤال
Use Newton's method to find the point of intersection of the graphs of 
and 
to within 0.00001 by solving the equation 
using 
and to within 0.00001 by solving the equation using سؤال
What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve 
at some point?
A)
B)
C)
D)
E)None of these
at some point?A)
B)
C)
D)
E)None of these
سؤال
A woman at a point A on the shore of a circular lake with radius 
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of 
and row a boat at 
. How should she proceed? (Find 
). Round the result, if necessary, to the nearest hundredth. 
A)
radians
B)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D)
radians
E)
radians
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth. A)
radiansB)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D)
radiansE)
radians سؤال
Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
The sum of two positive numbers is 
. What is the smallest possible value of the sum of their squares?
. What is the smallest possible value of the sum of their squares? سؤال
Find two positive numbers whose product is 
and whose sum is a minimum.
A)2, 72
B)3, 48
C)6, 24
D)
E)
and whose sum is a minimum.A)2, 72
B)3, 48
C)6, 24
D)
E)
سؤال
Consider the following problem: A farmer with 
ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
A)
B)
C)
D)
E)
ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?A)
B)
C)
D)
E)
سؤال
A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week. Find the demand function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A rectangular beam will be cut from a cylindrical log of radius 
inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. 
A)
in, 
in
B)
in, 
in
C)
in, 
in
D)
in, 
in
E)
in, 
in
inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. A)
in, inB)
in, inC)
in, inD)
in, inE)
in, in سؤال
A production editor decided that a promotional flyer should have a 1-in. margin at the top and the bottom, and a 
-in. margin on each side. The editor further stipulated that the flyer should have an area of 288 
. Determine the dimensions of the flyer that will result in the maximum printed area on the flyer. 
A)
in. 
in.
B)
in. 
in.
C)12 in.
24 in.
D)6 in.
48 in.
-in. margin on each side. The editor further stipulated that the flyer should have an area of 288 . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer. A)
in. in.B)
in. in.C)12 in.
24 in.D)6 in.
48 in. سؤال
Use Newton's method to approximate the zero of 
between 
and 
using 
. Continue until two successive approximations differ by less than 0.00001.
between and using . Continue until two successive approximations differ by less than 0.00001. سؤال
A piece of wire 
m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
A)
B)
C)
D)
E)
m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.A)
B)
C)
D)
E)
سؤال
Approximate the zero of 
in 
to within 0.00001.
in to within 0.00001. سؤال
Use Newton's method to find the zero of 
to within 0.00001 by solving the equation 
using 
to within 0.00001 by solving the equation using سؤال
Approximate the zero of 
in 
to within 0.00001.
in to within 0.00001. سؤال
A right circular cylinder is inscribed in a sphere of radius 
. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.
A)
B)
C)
D)
E)
. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.A)
B)
C)
D)
E)
سؤال
The average cost of producing x units of a commodity is given by the equation 
.
Find the marginal cost at a production level of 1,255 units.
.Find the marginal cost at a production level of 1,255 units.
سؤال
Find the dimensions of the rectangle enclosed in the semicircle 
with the largest possible area. 
A)
in. 
in.
B)5 in.
7 in.
C)
in. 
in.
D)
in. 
in.
with the largest possible area. A)
in. in.B)5 in.
7 in.C)
in. in.D)
in. in. سؤال
Find the dimensions of a rectangle of area 400 
that has the smallest possible perimeter.
A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
that has the smallest possible perimeter.A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
سؤال
Find the point on the line 
that is closest to the origin.
A)
B)
C)
D)
E)
that is closest to the origin.A)
B)
C)
D)
E)
سؤال
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 
million dollars. The additional cost of manufacturing each plane can be modeled by the function 
where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell 
.
Find the cost function.
million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell .Find the cost function.
سؤال
The manager of a 
-unit apartment complex knows from experience that all units will be occupied if the rent is 
per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 
increase in rent. What rent should the manager charge to maximize revenue?
-unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue? سؤال
If 
of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
of material is available to make a box with a square base and an open top, find the largest possible volume of the box. سؤال
For what values of 
does the curve have maximum and minimum points for the given function 
?
A)
B)
C)
D)
E)
does the curve have maximum and minimum points for the given function ?A)
B)
C)
D)
E)
سؤال
Find an equation of the line through the point 
that cuts off the least area from the first quadrant.
that cuts off the least area from the first quadrant. سؤال
Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length 
and width 
. 
and width . سؤال
What is the function of the graph? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A woman is on a lake in a rowboat located one mile form the closest point P of a straight shoreline (see the figure). She wishes to get to point Q, 8 miles along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 3 mph and walk at a speed of 4 mph, how should she pick the point R to get to Q as quickly as possible? How much time does she require?
8 mi 
8 mi سؤال
The owner of a ranch has 4000 yd of fencing with which to enclose a rectangular piece of grazing land situated along a straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is the area? 
سؤال
سؤال
For what values of 
does the curve have maximum and minimum points for the given function 
? Select the correct answer.
A)For
a parabola whose vertex 
, is the absolute maximum.For 
opens downward with one minimum points.For 
the graph opens upward, and has an absolute maximum at 
and no local minimum.
B)For
a parabola whose vertex 
, is the absolute maximum.For 
opens downward with two maximum points.For 
the graph opens upward, and has an absolute minimum at 
.
C)For
a parabola whose vertex 
, is the absolute maximum.For 
opens upward with two minimum points.For 
the graph opens downward, and has an absolute minimum at 
and no local minimum.
D)For
a parabola whose vertex 
, is the absolute maximum.For 
opens upward with two minimum points.For 
the graph opens downward, and has an absolute maximum at 
and no local minimum.
E)For
a parabola whose vertex 
, is the absolute maximum.For 
opens upward with two minimum points.For 
the graph opens downward, and has an absolute minimum at 
and no local minimum.
does the curve have maximum and minimum points for the given function ? Select the correct answer.A)For
a parabola whose vertex , is the absolute maximum.For opens downward with one minimum points.For the graph opens upward, and has an absolute maximum at and no local minimum.B)For
a parabola whose vertex , is the absolute maximum.For opens downward with two maximum points.For the graph opens upward, and has an absolute minimum at .C)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.D)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute maximum at and no local minimum.E)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum. سؤال
Select the correct graph for the given function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 
ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
ft, find the dimensions of the window so that the greatest possible amount of light is admitted. سؤال
Find the point on the line 
that is closest to the origin.
that is closest to the origin. سؤال
سؤال
What is the function of the graph? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner? 
سؤال
A fence 
ft tall runs parallel to a tall building at a distance of 
ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.
ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth. سؤال
سؤال
سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
using the curve-sketching guidelines. سؤال
Sketch the curve. 
A)
B)
C)
A)
B)
C)
سؤال
Sketch the curve. Find the equation of the slant asymptote. 
سؤال
An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by 
Sketch the graph of the function N, and interpret your result.
Sketch the graph of the function N, and interpret your result.
سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
سؤال
Find the horizontal and vertical asymptotes of the graph of the function 
.
A)HA
, VA 
B)HA
, VA none
C)HA
, VA none
D)HA
, VA 
.A)HA
, VA B)HA
, VA noneC)HA
, VA noneD)HA
, VA سؤال
Find the slant asymptote of the graph of 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
سؤال
A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by 
where 
is measured in meters per second. What is her terminal velocity? Hint: Evaluate 
A)
m/sec
B)
m/sec
C)
m/sec
D)
m/sec
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate A)
m/secB)
m/secC)
m/secD)
m/sec سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the limit. 
A)
B)0
C)
D)
A)
B)0
C)
D)
سؤال
Sketch the curve. 
A)
B)
C)
A)
B)
C)
سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
using the curve-sketching guidelines. سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
سؤال
Sketch the graph of the function 
on 
using the curve-sketching guidelines.
on using the curve-sketching guidelines. سؤال
Sketch the graph of the function 
using the curve-sketching guidelines.
using the curve-sketching guidelines. سؤال
Sketch the curve. 
, 
A)
B)
C)
, A)
B)
C)
سؤال
Let 
and 
be polynomials. Find 
if the degree of 
is 
and the degree of 
is 
.
A)
B)
C)
D)
E)
and be polynomials. Find if the degree of is and the degree of is .A)
B)
C)
D)
E)
سؤال
Find the slant asymptote of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 3: Applications of Differentiation
1
Find the most general antiderivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Find f.
3
A particle moves along a straight line with velocity function and its initial displacement is . Find its position function.
and its initial displacement is . Find its position function.
4
A company estimates that the marginal cost (in dollars per item) of producing items is . If the cost of producing one item is $560 find the cost of producing 400 items.
. If the cost of producing one item is $560 find the cost of producing 400 items. فتح الحزمة
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5
Find the most general antiderivative of the function.
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6
Find the most general antiderivative of the function.
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7
A ballast is dropped from a stationary hot-air balloon that is at an altitude of 256 ft. Find (a) an expression for the altitude of the ballast after t seconds, (b) the time when it strikes the ground, and (c) its velocity when it strikes the ground. (Disregard air resistance and take .)
.) فتح الحزمة
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8
What constant acceleration is required to increase the speed of a car from 30 ft/s to 45 ft/s in
4 s?
4 s?
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9
A car braked with a constant deceleration of , producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?
, producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied? فتح الحزمة
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10
To what constant deceleration would a car moving along a straight road be subjected if the car were brought to rest from a speed of 86 ft/sec in 7 sec? What would the stopping distance be?
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11
Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is , find f (1) .
A)11
B)1
C)0
D)12
E)6
is , find f (1) .A)11
B)1
C)0
D)12
E)6
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12
Estimate the value of by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.
A)1.71
B)2.2662
C)2.2361
D)1.6535
by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.A)1.71
B)2.2662
C)2.2361
D)1.6535
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13
Suppose the line is tangent to the curve when . If Newton's method is used to locate a root of the equation and the initial approximation is , find the second approximation .
is tangent to the curve when . If Newton's method is used to locate a root of the equation and the initial approximation is , find the second approximation . فتح الحزمة
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14
Evaluate , and tell whether its antiderivative F is increasing or decreasing at the point radians.
A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
, and tell whether its antiderivative F is increasing or decreasing at the point radians.A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
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15
Use Newton's method to approximate the zero of between and using . Continue until two successive approximations differ by less than 0.00001.
A)0.16904
B)0.11154
C)0.23624
D)0.07984
between and using . Continue until two successive approximations differ by less than 0.00001.A)0.16904
B)0.11154
C)0.23624
D)0.07984
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16
Use Newton's method to approximate the indicated root of in the interval , correct to six decimal places.
Use as the initial approximation.
in the interval , correct to six decimal places.Use
as the initial approximation. فتح الحزمة
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17
The size of the monthly repayment k that amortizes a loan of A dollars in N years at an interest rate of r per year, compounded monthly, on the unpaid balance is given by The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.
A)8.7%
B)7.7%
C)6.7%
D)5.7%
The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.A)8.7%
B)7.7%
C)6.7%
D)5.7%
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18
Find the position function of a particle moving along a coordinate line that satisfies the given condition. , s(1) = -1
, s(1) = -1 فتح الحزمة
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19
Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)
to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.) فتح الحزمة
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20
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. , s(0) = 5, v(0) = 0
, s(0) = 5, v(0) = 0 فتح الحزمة
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21
Use Newton's method to find the point of intersection of the graphs of and to within 0.00001 by solving the equation using
and to within 0.00001 by solving the equation using فتح الحزمة
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22
What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve at some point?
A)
B)
C)
D)
E)None of these
at some point?A)
B)
C)
D)
E)None of these
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23
A woman at a point A on the shore of a circular lake with radius wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth.
A) radians
B)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D) radians
E) radians
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth. A)
radiansB)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D)
radiansE)
radians فتح الحزمة
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24
Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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25
The sum of two positive numbers is . What is the smallest possible value of the sum of their squares?
. What is the smallest possible value of the sum of their squares? فتح الحزمة
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26
Find two positive numbers whose product is and whose sum is a minimum.
A)2, 72
B)3, 48
C)6, 24
D)
E)
and whose sum is a minimum.A)2, 72
B)3, 48
C)6, 24
D)
E)
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27
Consider the following problem: A farmer with ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
A)
B)
C)
D)
E)
ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?A)
B)
C)
D)
E)
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28
A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week. Find the demand function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
A rectangular beam will be cut from a cylindrical log of radius inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.
A) in, in
B) in, in
C) in, in
D) in, in
E) in, in
inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. A)
in, inB)
in, inC)
in, inD)
in, inE)
in, in فتح الحزمة
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30
A production editor decided that a promotional flyer should have a 1-in. margin at the top and the bottom, and a -in. margin on each side. The editor further stipulated that the flyer should have an area of 288 . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer.
A) in. in.
B) in. in.
C)12 in. 24 in.
D)6 in. 48 in.
-in. margin on each side. The editor further stipulated that the flyer should have an area of 288 . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer. A)
in. in.B)
in. in.C)12 in.
24 in.D)6 in.
48 in. فتح الحزمة
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31
Use Newton's method to approximate the zero of between and using . Continue until two successive approximations differ by less than 0.00001.
between and using . Continue until two successive approximations differ by less than 0.00001. فتح الحزمة
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32
A piece of wire m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
A)
B)
C)
D)
E)
m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.A)
B)
C)
D)
E)
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33
Approximate the zero of in to within 0.00001.
in to within 0.00001. فتح الحزمة
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34
Use Newton's method to find the zero of to within 0.00001 by solving the equation using
to within 0.00001 by solving the equation using فتح الحزمة
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35
Approximate the zero of in to within 0.00001.
in to within 0.00001. فتح الحزمة
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36
A right circular cylinder is inscribed in a sphere of radius . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.
A)
B)
C)
D)
E)
. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.A)
B)
C)
D)
E)
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37
The average cost of producing x units of a commodity is given by the equation .
Find the marginal cost at a production level of 1,255 units.
.Find the marginal cost at a production level of 1,255 units.
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38
Find the dimensions of the rectangle enclosed in the semicircle with the largest possible area.
A) in. in.
B)5 in. 7 in.
C) in. in.
D) in. in.
with the largest possible area. A)
in. in.B)5 in.
7 in.C)
in. in.D)
in. in. فتح الحزمة
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39
Find the dimensions of a rectangle of area 400 that has the smallest possible perimeter.
A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
that has the smallest possible perimeter.A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
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40
Find the point on the line that is closest to the origin.
A)
B)
C)
D)
E)
that is closest to the origin.A)
B)
C)
D)
E)
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41
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell .
Find the cost function.
million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell .Find the cost function.
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42
The manager of a -unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue?
-unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue? فتح الحزمة
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43
If of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
of material is available to make a box with a square base and an open top, find the largest possible volume of the box. فتح الحزمة
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44
For what values of does the curve have maximum and minimum points for the given function ?
A)
B)
C)
D)
E)
does the curve have maximum and minimum points for the given function ?A)
B)
C)
D)
E)
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45
Find an equation of the line through the point that cuts off the least area from the first quadrant.
that cuts off the least area from the first quadrant. فتح الحزمة
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46
Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length and width .
and width . فتح الحزمة
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47
What is the function of the graph?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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48
A woman is on a lake in a rowboat located one mile form the closest point P of a straight shoreline (see the figure). She wishes to get to point Q, 8 miles along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 3 mph and walk at a speed of 4 mph, how should she pick the point R to get to Q as quickly as possible? How much time does she require?
8 mi
8 mi فتح الحزمة
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49
The owner of a ranch has 4000 yd of fencing with which to enclose a rectangular piece of grazing land situated along a straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is the area?
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50
A baseball team plays in a stadium that holds 56,000 spectators. With ticket prices at $9, the average attendance had been 32,000. When ticket prices were lowered to $8, the average attendance rose to 36,000. How should ticket prices be set to maximize revenue? Assume the demand function is linear.
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51
For what values of does the curve have maximum and minimum points for the given function ? Select the correct answer.
A)For a parabola whose vertex , is the absolute maximum.For opens downward with one minimum points.For the graph opens upward, and has an absolute maximum at and no local minimum.
B)For a parabola whose vertex , is the absolute maximum.For opens downward with two maximum points.For the graph opens upward, and has an absolute minimum at .
C)For a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.
D)For a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute maximum at and no local minimum.
E)For a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.
does the curve have maximum and minimum points for the given function ? Select the correct answer.A)For
a parabola whose vertex , is the absolute maximum.For opens downward with one minimum points.For the graph opens upward, and has an absolute maximum at and no local minimum.B)For
a parabola whose vertex , is the absolute maximum.For opens downward with two maximum points.For the graph opens upward, and has an absolute minimum at .C)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.D)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute maximum at and no local minimum.E)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum. فتح الحزمة
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52
Select the correct graph for the given function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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53
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
ft, find the dimensions of the window so that the greatest possible amount of light is admitted. فتح الحزمة
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54
Find the point on the line that is closest to the origin.
that is closest to the origin. فتح الحزمة
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55
A rectangular box having a top and a square base is to be constructed at a cost of $1. If the material for the bottom costs $0.35 per square foot, the material for the top costs $0.15 per square foot, and the material for the sides costs $0.20 per square foot, find the dimensions and volume of the box of maximum volume that can be constructed.
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56
What is the function of the graph?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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57
A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?
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58
A fence ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.
ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth. فتح الحزمة
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59
Find two numbers whose difference is 170 and whose product is a minimum.
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60
If an open box is made from a metal sheet 9 in. square by cutting out identical squares from each corner an bending up the resulting flaps, determine the dimensions of the box with the largest volume that can be made.
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61
Sketch the graph of the function using the curve-sketching guidelines.
using the curve-sketching guidelines. فتح الحزمة
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62
Sketch the curve.
A)
B)
C)
A)
B)
C)
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63
Sketch the curve. Find the equation of the slant asymptote.
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64
An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by
Sketch the graph of the function N, and interpret your result.
Sketch the graph of the function N, and interpret your result.
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65
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
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66
Find the horizontal and vertical asymptotes of the graph of the function .
A)HA , VA
B)HA , VA none
C)HA , VA none
D)HA , VA
.A)HA
, VA B)HA
, VA noneC)HA
, VA noneD)HA
, VA فتح الحزمة
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67
Find the slant asymptote of the graph of using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
فتح الحزمة
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68
A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second. What is her terminal velocity? Hint: Evaluate
A) m/sec
B) m/sec
C) m/sec
D) m/sec
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate A)
m/secB)
m/secC)
m/secD)
m/sec فتح الحزمة
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69
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
70
Find the limit.
A)
B)0
C)
D)
A)
B)0
C)
D)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
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k this deck
71
Sketch the curve.
A)
B)
C)
A)
B)
C)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
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k this deck
72
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
73
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
74
Sketch the graph of the function using the curve-sketching guidelines.
using the curve-sketching guidelines. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
75
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
76
Sketch the graph of the function on using the curve-sketching guidelines.
on using the curve-sketching guidelines. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
77
Sketch the graph of the function using the curve-sketching guidelines.
using the curve-sketching guidelines. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
78
Sketch the curve. ,
A)
B)
C)
, A)
B)
C)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
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k this deck
79
Let and be polynomials. Find if the degree of is and the degree of is .
A)
B)
C)
D)
E)
and be polynomials. Find if the degree of is and the degree of is .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
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k this deck
80
Find the slant asymptote of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
فتح الحزمة
k this deck
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 153 في هذه المجموعة.
