تكلم مع الذكاء الاصطناعي
Deck 2: Limits and Their Properties
ملء الشاشة (f)
سؤال
Suppose that 
. Find the following limit. 
A) -1
B) 1
C) 3
D) 0
E) 2
. Find the following limit. A) -1
B) 1
C) 3
D) 0
E) 2
سؤال
Find the limit (if it exists). 
A) 0
B)
C)
D)
E) Limit does not exist.
A) 0
B)
C)
D)
E) Limit does not exist.
سؤال
Suppose that 
. Find the following limit. 
A) -5
B) -55
C) 55
D) -11c
E) -11
. Find the following limit. A) -5
B) -55
C) 55
D) -11c
E) -11
سؤال
Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point. 
7
A)
B)
C)
D)
E) does not exist
7
A)
B)
C)
D)
E) does not exist
سؤال
Use a graphing utility to graph the function 
and determine the following one-sided limit. 
A)
B) 6
C) -6
D)
E) 0
and determine the following one-sided limit. A)
B) 6
C) -6
D)
E) 0
سؤال
سؤال
Find the constant a and b such that the function 
Is continuous on the entire real line.
A) a = 3, b = 0
B) a = 3, b = -3
C) a = -3, b = -3
D) a = -3, b = 3
E) a = 3, b = 3
Is continuous on the entire real line.
A) a = 3, b = 0
B) a = 3, b = -3
C) a = -3, b = -3
D) a = -3, b = 3
E) a = 3, b = 3
سؤال
Find the limit. 
A) 1
B)
C) 0
D)
E) -1
A) 1
B)
C) 0
D)
E) -1
سؤال
Find 
where 
.
A) 1
B) 4
C) -5
D) 1
E) Limit does not exist.
where . A) 1
B) 4
C) -5
D) 1
E) Limit does not exist.
سؤال
A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of 
where x is the distance between the base of the ladder and the house. Find the limit of r as 
. 
A)
B) 50
C) 0
D)
E) 25
where x is the distance between the base of the ladder and the house. Find the limit of r as . A)
B) 50
C) 0
D)
E) 25
سؤال
Find the vertical asymptotes (if any) of the function 
.
A)
B)
C)
D)
E) no vertical asymptotes
. A)
B)
C)
D)
E) no vertical asymptotes
سؤال
سؤال
A long distance phone service charges $0.35 for the first 8 minutes and $0.05 for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Suppose that 
and 
. Find the following limit. 
A)
B)
C)
D)
E) does not exist
and . Find the following limit. A)
B)
C)
D)
E) does not exist
سؤال
Find all the vertical asymptotes (if any) of the graph of the function 
.
A) x = -1
B) x = 5
C) x = 1, -1
D) x = 1
E) no vertical asymptotes
. A) x = -1
B) x = 5
C) x = 1, -1
D) x = 1
E) no vertical asymptotes
سؤال
Use the graph to find the limit. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Let 
Determine the following limit.
Determine the following limit. سؤال
Determine the limit (if it exists). 
A) 0
B) 1
C) 2
D) ∞
E) does not exist
A) 0
B) 1
C) 2
D) ∞
E) does not exist
سؤال
Find the x-values (if any) at which the function 
is not continuous. Which of the discontinuities are removable?
A) 10 and -10, removable
B) discontinuous everywhere 0 00
C) continuous everywhere 0 00
D) 10 and -10, not removable
E) 0, removable
is not continuous. Which of the discontinuities are removable? A) 10 and -10, removable
B) discontinuous everywhere 0 00
C) continuous everywhere 0 00
D) 10 and -10, not removable
E) 0, removable
سؤال
Let 
Determine the following limit.
Determine the following limit. سؤال
Find the limit (if it exists). Note that 
represents the greatest integer function. 
A) -109
B) 119
C) -119
D) 109
E) does not exist
represents the greatest integer function. A) -109
B) 119
C) -119
D) 109
E) does not exist
سؤال
Complete the table and use the result to estimate the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the value of c guaranteed by the Intermediate Value Theorem. 
A) 7
B) 2
C) 1
D) 5
E) 6
A) 7
B) 2
C) 1
D) 5
E) 6
سؤال
Suppose that 
and 
. Find the following limit. 
A) 0
B) -4
C) -9
D) -17
E) 52
and . Find the following limit. A) 0
B) -4
C) -9
D) -17
E) 52
سؤال
Find the following limit if it exists: 
. Use 
when appropriate.
A)
B) -4
C) 1
D)
E) does not exist
. Use when appropriate. A)
B) -4
C) 1
D)
E) does not exist
سؤال
A petrol car is parked 35 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 
revolution per second. The rate at which the light beam moves along the wall is 
ft/sec. Find the rate r when 
is 
. 
A)
ft/sec
B)
ft/sec
C)
ft/sec
D)
ft/sec
E)
ft/sec
revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the rate r when is . A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec سؤال
Determine the limit (if it exists). 
A) 8
B) 1
C) 0
D) -2
E) does not exist
A) 8
B) 1
C) 0
D) -2
E) does not exist
سؤال
A petrol car is parked 65 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 
revolution per second. The rate at which the light beam moves along the wall is 
ft/sec. Find the limit of r as 
. 
A)
B)
C) 0
D) 65
E)
revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the limit of r as . A)
B)
C) 0
D) 65
E)
سؤال
Find the lmit. 
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
سؤال
Find the x-values (if any) at which 
is not continuous.
A) f(x) is not continuous at x = 0 and f(x) has a removable discontinuity at x = 0.
B) f(x) is not continuous at x = 0, -2 and both the discontinuities are nonremovable.
C) f(x) is not continuous at x = -2 and f(x) has a removable discontinuity at x = -2.
D) f(x) is not continuous at x = 0, -2 and f(x) has a removable discontinuity at x = 0.
E) f(x) is continuous for all real x.
is not continuous. A) f(x) is not continuous at x = 0 and f(x) has a removable discontinuity at x = 0.
B) f(x) is not continuous at x = 0, -2 and both the discontinuities are nonremovable.
C) f(x) is not continuous at x = -2 and f(x) has a removable discontinuity at x = -2.
D) f(x) is not continuous at x = 0, -2 and f(x) has a removable discontinuity at x = 0.
E) f(x) is continuous for all real x.
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
A cyclist is riding on a path whose elevation is modeled by the function
wherexand 
are measured in miles. Find the rate of change of elevation when x= 3. 
A) precalculus, 0.06
B) calculus, 0.18
C) calculus, 0.36
D) calculus, 0.06
E) precalculus, 0.18
A cyclist is riding on a path whose elevation is modeled by the function
wherexand are measured in miles. Find the rate of change of elevation when x= 3. A) precalculus, 0.06
B) calculus, 0.18
C) calculus, 0.36
D) calculus, 0.06
E) precalculus, 0.18
سؤال
A 30-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of 
, where x is the distance between the base of the ladder and the house. Find the rate r when x is 18 feet. 
A) r =
ft/sec
B) r =
ft/sec
C)
ft/sec
D) r =
ft/sec
E) r =
ft/sec
, where x is the distance between the base of the ladder and the house. Find the rate r when x is 18 feet. A) r =
ft/secB) r =
ft/secC)
ft/secD) r =
ft/secE) r =
ft/sec سؤال
Use the rectangles in the following graph to approximate the area of the region bounded by 
. 
A) 0.9481
B) 1.8961
C) 3.7922
D) 1.4221
E) 1.2704
. A) 0.9481
B) 1.8961
C) 3.7922
D) 1.4221
E) 1.2704
سؤال
Let 
and 
. Find the limit. 
A)
B)
C)
D)
E)
and . Find the limit. A)
B)
C)
D)
E)
سؤال
Find the limit (if it exists). 
A) Limit does not exist.
B) 0
C) 3
D) 4
E) 9
A) Limit does not exist.
B) 0
C) 3
D) 4
E) 9
سؤال
Find the limit. 
A) 1
B) 0
C) -1
D)
E)
A) 1
B) 0
C) -1
D)
E)
سؤال
سؤال
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).
A) precalculus , 120
B) calculus , 180
C) precalculus , 60
D) precalculus , 180
E) calculus , 120
Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).
A) precalculus , 120
B) calculus , 180
C) precalculus , 60
D) precalculus , 180
E) calculus , 120
سؤال
Find the x-values (if any) at which the function 
is not continuous. Which of the discontinuities are removable?
A) no points of discontinuity
B) x = -9 (not removable), x = -5 (removable)
C) x = -9 (removable), x = -5 (not removable)
D) no points of continuity
E) x = -9 (not removable), x = -5 (not removable)
is not continuous. Which of the discontinuities are removable? A) no points of discontinuity
B) x = -9 (not removable), x = -5 (removable)
C) x = -9 (removable), x = -5 (not removable)
D) no points of continuity
E) x = -9 (not removable), x = -5 (not removable)
سؤال
Suppose that 
and 
. Find the following limit. 
A) -3
B) 5
C) 24
D) -11
E) 0
and . Find the following limit. A) -3
B) 5
C) 24
D) -11
E) 0
سؤال
سؤال
Use the rectangles in the graph given below to approximate the area of the region bounded by 
. Round your answer to three decimal places. 
A) 2.481 units2
B) 6.371units2
C) 3.585units2
D) 6.872units2
E) 6.903units2
. Round your answer to three decimal places. A) 2.481 units2
B) 6.371units2
C) 3.585units2
D) 6.872units2
E) 6.903units2
سؤال
Use the graph as shown to determine the following limits, and discuss the continuity of the function at x= 4.
(i)
(ii) 
(iii) 
A) 1, 1, 1, not continuous
B) 2, 2, 2, continuous
C) 1, 1, 1, continuous
D) 2, 2, 2, not continuous
E) 0, 0, 0, not continuous
(i)
(ii) (iii) A) 1, 1, 1, not continuous
B) 2, 2, 2, continuous
C) 1, 1, 1, continuous
D) 2, 2, 2, not continuous
E) 0, 0, 0, not continuous
سؤال
Find the limit. 
A)
B)
C) -12
D) 6
E) 12
A)
B)
C) -12
D) 6
E) 12
سؤال
Find the limit (if it exists). 
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
سؤال
Find the limit (if it exists). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Suppose that 
and 
. Find the following limit. 
A) 9
B) -3
C) -21
D) -12
E) 108
and . Find the following limit. A) 9
B) -3
C) -21
D) -12
E) 108
سؤال
Use the graph as shown to determine the following limits, and discuss the continuity of the function at x= -4.
(i)
(ii) 
(iii) 
A) 2, 2, 2, continuous
B) 1, 1, 1, not continuous
C) 2, 2, 2, not continuous
D) -4, -4, -4, continuous
E) 1, 1, 1, continuous
(i)
(ii) (iii) A) 2, 2, 2, continuous
B) 1, 1, 1, not continuous
C) 2, 2, 2, not continuous
D) -4, -4, -4, continuous
E) 1, 1, 1, continuous
سؤال
Find the x-values (if any) at which 
is not continuous.
A) f(x) is not continuous at x = -2 and the discontinuity is nonremovable.
B) f(x) is not continuous at x = 0 and the discontinuity is removable.
C) f(x) is continuous for all real x.
D) f(x) is not continuous at x = -2 and the discontinuity is removable.
E) f(x) is not continuous at x = 0, 2 and x = 0 is a removable discontinuity.
is not continuous. A) f(x) is not continuous at x = -2 and the discontinuity is nonremovable.
B) f(x) is not continuous at x = 0 and the discontinuity is removable.
C) f(x) is continuous for all real x.
D) f(x) is not continuous at x = -2 and the discontinuity is removable.
E) f(x) is not continuous at x = 0, 2 and x = 0 is a removable discontinuity.
سؤال
Find the limit (if it exists). 
A)
B)
C) 0
D)
E) Limit does not exist
A)
B)
C) 0
D)
E) Limit does not exist
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Complete the table and use the result to estimate the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the value of c guaranteed by the Intermediate Value Theorem. 
A) 1
B) 4
C) 6
D) 2
E) 5
A) 1
B) 4
C) 6
D) 2
E) 5
سؤال
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
A cyclist is riding on a path whose elevation is modeled by the function
where x and 
are measured in miles. Find the rate of change of elevation when x = 3.
A) calculus, 0.72
B) precalculus, 0.12
C) calculus, 0.12
D) precalculus, 0.72
E) precalculus, 0.37
A cyclist is riding on a path whose elevation is modeled by the function
where x and are measured in miles. Find the rate of change of elevation when x = 3.
A) calculus, 0.72
B) precalculus, 0.12
C) calculus, 0.12
D) precalculus, 0.72
E) precalculus, 0.37
سؤال
سؤال
Use a graphing utility to graph the function 
and determine the one-sided limit 
.
A)
B)
C) 0
D) 3
E) 2
and determine the one-sided limit . A)
B)
C) 0
D) 3
E) 2
سؤال
Find the x-values (if any) at which the function f(x) = 11x2 - 5x - 5 is not continuous. Which of the discontinuities are removable?
A) x = 2, removable
B) x = 0, removable
C)
D) continuous everywhere
E)
A) x = 2, removable
B) x = 0, removable
C)
D) continuous everywhere
E)
سؤال
Find the vertical asymptotes (if any) of the function 
.
A) x = 2
B) x = 6
C) x = -6
D) x = 12
E) x = -2
. A) x = 2
B) x = 6
C) x = -6
D) x = 12
E) x = -2
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
Find the limit (if it exists). Note that 
represents the greatest integer function. 
A) 13
B) Limit does not exist.
C) 12
D) 0
E) 11
represents the greatest integer function. A) 13
B) Limit does not exist.
C) 12
D) 0
E) 11
سؤال
Let 
and 
. Find the limit. 
A)
B)
C)
D)
E)
and . Find the limit. A)
B)
C)
D)
E)
سؤال
Find the constant a such that the function 
Is continuous on the entire real line.
A) 1
B) -7
C) 7
D) 14
E) -14
Is continuous on the entire real line.
A) 1
B) -7
C) 7
D) 14
E) -14
سؤال
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Find the distance traveled in 13 seconds by an object moving with a velocity of
feet per second.
A) calculus, 162.3521 ft
B) precalculus, 163.7021 ft
C) calculus, 158.9412 ft
D) precalculus, 158.9412 ft
E) precalculus, 162.3521 ft
Find the distance traveled in 13 seconds by an object moving with a velocity of
feet per second.
A) calculus, 162.3521 ft
B) precalculus, 163.7021 ft
C) calculus, 158.9412 ft
D) precalculus, 158.9412 ft
E) precalculus, 162.3521 ft
سؤال
Determine the limit (if it exists). 
A) 0
B) 56
C) 11
D) 28
E) does not exist
A) 0
B) 56
C) 11
D) 28
E) does not exist
سؤال
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Find the area of the shaded region.
A) calculus , 15
B) precalculus , 15
C) precalculus , 18
D) calculus , 22
E) precalculus , 22
Find the area of the shaded region.
A) calculus , 15
B) precalculus , 15
C) precalculus , 18
D) calculus , 22
E) precalculus , 22
سؤال
Use the graph to determine the following limits, and discuss the continuity of the function at x = -4. (i) 
(ii) 
(iii) 
A) 2, -2, does not exist, not continuous
B) 2, 0, does not exist, not continuous
C) 0, 2, does not exist, not continuous
D) -4, 0, does not exist, not continuous
E) 0, 2, 0, continuous
(ii) (iii) A) 2, -2, does not exist, not continuous
B) 2, 0, does not exist, not continuous
C) 0, 2, does not exist, not continuous
D) -4, 0, does not exist, not continuous
E) 0, 2, 0, continuous
سؤال
Consider the length of the graph of 
from 
to 
. Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places. 
A) 7.76
B) 9.77
C) 7.07
D) 9.9
E) 8.76
from to . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places. A) 7.76
B) 9.77
C) 7.07
D) 9.9
E) 8.76
سؤال
Find all values of c such that f is continuous on (-∞,∞). 
A) c = 2
B) c = 0
C)
D)
E)
A) c = 2
B) c = 0
C)
D)
E)
سؤال
Find all vertical asymptotes (if any) of the function 
A) x = 1, 5
B) x = 1, 5, -4
C) x = -1, -5
D) x = 5
E) x = -5
A) x = 1, 5
B) x = 1, 5, -4
C) x = -1, -5
D) x = 5
E) x = -5
سؤال
Complete the table and use the result to estimate the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the rectangles in the following graph to approximate the area of the region bounded by 
. 
A) 3.9485
B) 2.6323
C) 1.9742
D) 1.4807
E) 0.9871
. A) 3.9485
B) 2.6323
C) 1.9742
D) 1.4807
E) 0.9871
سؤال
Find the limit (if it exists). 
A) 10
B)
C)
D)
E)
.
A) 10
B)
C)
D)
E)
. سؤال
Find the limit (if it exists). 
A)
B) 0
C) Limit does not exist.
D)
E)
A)
B) 0
C) Limit does not exist.
D)
E)
سؤال
Let 
and 
. Find the limit. 
A)
B)
C)
D)
E)
and . Find the limit. A)
B)
C)
D)
E)
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all the vertical asymptotes (if any) of the graph of the function 
.
A) x = -2
B) x = 4
C) x = 0
D) x = 4, x = 0
E) no vertical asymptotes
. A) x = -2
B) x = 4
C) x = 0
D) x = 4, x = 0
E) no vertical asymptotes
سؤال
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العب
ملء الشاشة (f)
Deck 2: Limits and Their Properties
1
Suppose that . Find the following limit.
A) -1
B) 1
C) 3
D) 0
E) 2
. Find the following limit. A) -1
B) 1
C) 3
D) 0
E) 2
B
2
Find the limit (if it exists).
A) 0
B)
C)
D)
E) Limit does not exist.
A) 0
B)
C)
D)
E) Limit does not exist.
D
3
Suppose that . Find the following limit.
A) -5
B) -55
C) 55
D) -11c
E) -11
. Find the following limit. A) -5
B) -55
C) 55
D) -11c
E) -11
C
4
Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point. 7
A)
B)
C)
D)
E) does not exist
7
A)
B)
C)
D)
E) does not exist
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5
Use a graphing utility to graph the function and determine the following one-sided limit.
A)
B) 6
C) -6
D)
E) 0
and determine the following one-sided limit. A)
B) 6
C) -6
D)
E) 0
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6
A ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8.5 centimeters and 9.5 centimeters how can the radius vary? Round your answer to five decimal places.
A) Radius can vary between 7.32046 centimeters and 9.14424 centimeters.
B) Radius can vary between 1.64488 centimeters and 1.73895 centimeters.
C) Radius can vary between 1.35282 centimeters and 1.51197 centimeters.
D) Radius can vary between 2.70563 centimeters and 3.02394 centimeters.
E) Radius can vary between 0.93239 centimeter and 1.93239 centimeters.
A) Radius can vary between 7.32046 centimeters and 9.14424 centimeters.
B) Radius can vary between 1.64488 centimeters and 1.73895 centimeters.
C) Radius can vary between 1.35282 centimeters and 1.51197 centimeters.
D) Radius can vary between 2.70563 centimeters and 3.02394 centimeters.
E) Radius can vary between 0.93239 centimeter and 1.93239 centimeters.
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7
Find the constant a and b such that the function
Is continuous on the entire real line.
A) a = 3, b = 0
B) a = 3, b = -3
C) a = -3, b = -3
D) a = -3, b = 3
E) a = 3, b = 3
Is continuous on the entire real line.
A) a = 3, b = 0
B) a = 3, b = -3
C) a = -3, b = -3
D) a = -3, b = 3
E) a = 3, b = 3
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8
Find the limit.
A) 1
B)
C) 0
D)
E) -1
A) 1
B)
C) 0
D)
E) -1
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9
Find where .
A) 1
B) 4
C) -5
D) 1
E) Limit does not exist.
where . A) 1
B) 4
C) -5
D) 1
E) Limit does not exist.
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10
A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of where x is the distance between the base of the ladder and the house. Find the limit of r as .
A)
B) 50
C) 0
D)
E) 25
where x is the distance between the base of the ladder and the house. Find the limit of r as . A)
B) 50
C) 0
D)
E) 25
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11
Find the vertical asymptotes (if any) of the function .
A)
B)
C)
D)
E) no vertical asymptotes
. A)
B)
C)
D)
E) no vertical asymptotes
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12
A sphere has a volume of 4.12 cubic inches. What is the radius of the sphere? Round your answer to four decimal places.
A) 0.9945 inch
B) 1.5787 inches
C) 0.9918 inch
D) 1.9835 inches
E) 1.7988 inches
A) 0.9945 inch
B) 1.5787 inches
C) 0.9918 inch
D) 1.9835 inches
E) 1.7988 inches
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13
A long distance phone service charges $0.35 for the first 8 minutes and $0.05 for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Suppose that and . Find the following limit.
A)
B)
C)
D)
E) does not exist
and . Find the following limit. A)
B)
C)
D)
E) does not exist
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15
Find all the vertical asymptotes (if any) of the graph of the function .
A) x = -1
B) x = 5
C) x = 1, -1
D) x = 1
E) no vertical asymptotes
. A) x = -1
B) x = 5
C) x = 1, -1
D) x = 1
E) no vertical asymptotes
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16
Use the graph to find the limit.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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17
Let Determine the following limit.
Determine the following limit. فتح الحزمة
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18
Determine the limit (if it exists).
A) 0
B) 1
C) 2
D) ∞
E) does not exist
A) 0
B) 1
C) 2
D) ∞
E) does not exist
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19
Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?
A) 10 and -10, removable
B) discontinuous everywhere 0 00
C) continuous everywhere 0 00
D) 10 and -10, not removable
E) 0, removable
is not continuous. Which of the discontinuities are removable? A) 10 and -10, removable
B) discontinuous everywhere 0 00
C) continuous everywhere 0 00
D) 10 and -10, not removable
E) 0, removable
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20
Let Determine the following limit.
Determine the following limit. فتح الحزمة
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21
Find the limit (if it exists). Note that represents the greatest integer function.
A) -109
B) 119
C) -119
D) 109
E) does not exist
represents the greatest integer function. A) -109
B) 119
C) -119
D) 109
E) does not exist
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22
Complete the table and use the result to estimate the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
Find the value of c guaranteed by the Intermediate Value Theorem.
A) 7
B) 2
C) 1
D) 5
E) 6
A) 7
B) 2
C) 1
D) 5
E) 6
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24
Suppose that and . Find the following limit.
A) 0
B) -4
C) -9
D) -17
E) 52
and . Find the following limit. A) 0
B) -4
C) -9
D) -17
E) 52
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25
Find the following limit if it exists: . Use when appropriate.
A)
B) -4
C) 1
D)
E) does not exist
. Use when appropriate. A)
B) -4
C) 1
D)
E) does not exist
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26
A petrol car is parked 35 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the rate r when is .
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec
revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the rate r when is . A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec فتح الحزمة
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27
Determine the limit (if it exists).
A) 8
B) 1
C) 0
D) -2
E) does not exist
A) 8
B) 1
C) 0
D) -2
E) does not exist
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28
A petrol car is parked 65 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the limit of r as .
A)
B)
C) 0
D) 65
E)
revolution per second. The rate at which the light beam moves along the wall is ft/sec. Find the limit of r as . A)
B)
C) 0
D) 65
E)
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29
Find the lmit.
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
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30
Find the x-values (if any) at which is not continuous.
A) f(x) is not continuous at x = 0 and f(x) has a removable discontinuity at x = 0.
B) f(x) is not continuous at x = 0, -2 and both the discontinuities are nonremovable.
C) f(x) is not continuous at x = -2 and f(x) has a removable discontinuity at x = -2.
D) f(x) is not continuous at x = 0, -2 and f(x) has a removable discontinuity at x = 0.
E) f(x) is continuous for all real x.
is not continuous. A) f(x) is not continuous at x = 0 and f(x) has a removable discontinuity at x = 0.
B) f(x) is not continuous at x = 0, -2 and both the discontinuities are nonremovable.
C) f(x) is not continuous at x = -2 and f(x) has a removable discontinuity at x = -2.
D) f(x) is not continuous at x = 0, -2 and f(x) has a removable discontinuity at x = 0.
E) f(x) is continuous for all real x.
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31
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
A cyclist is riding on a path whose elevation is modeled by the function wherexand are measured in miles. Find the rate of change of elevation when x= 3.
A) precalculus, 0.06
B) calculus, 0.18
C) calculus, 0.36
D) calculus, 0.06
E) precalculus, 0.18
A cyclist is riding on a path whose elevation is modeled by the function
wherexand are measured in miles. Find the rate of change of elevation when x= 3. A) precalculus, 0.06
B) calculus, 0.18
C) calculus, 0.36
D) calculus, 0.06
E) precalculus, 0.18
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33
A 30-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of , where x is the distance between the base of the ladder and the house. Find the rate r when x is 18 feet.
A) r = ft/sec
B) r = ft/sec
C) ft/sec
D) r = ft/sec
E) r = ft/sec
, where x is the distance between the base of the ladder and the house. Find the rate r when x is 18 feet. A) r =
ft/secB) r =
ft/secC)
ft/secD) r =
ft/secE) r =
ft/sec فتح الحزمة
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34
Use the rectangles in the following graph to approximate the area of the region bounded by .
A) 0.9481
B) 1.8961
C) 3.7922
D) 1.4221
E) 1.2704
. A) 0.9481
B) 1.8961
C) 3.7922
D) 1.4221
E) 1.2704
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35
Let and . Find the limit.
A)
B)
C)
D)
E)
and . Find the limit. A)
B)
C)
D)
E)
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36
Find the limit (if it exists).
A) Limit does not exist.
B) 0
C) 3
D) 4
E) 9
A) Limit does not exist.
B) 0
C) 3
D) 4
E) 9
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37
Find the limit.
A) 1
B) 0
C) -1
D)
E)
A) 1
B) 0
C) -1
D)
E)
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38
Determine the following limit.
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39
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).
A) precalculus , 120
B) calculus , 180
C) precalculus , 60
D) precalculus , 180
E) calculus , 120
Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).
A) precalculus , 120
B) calculus , 180
C) precalculus , 60
D) precalculus , 180
E) calculus , 120
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40
Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?
A) no points of discontinuity
B) x = -9 (not removable), x = -5 (removable)
C) x = -9 (removable), x = -5 (not removable)
D) no points of continuity
E) x = -9 (not removable), x = -5 (not removable)
is not continuous. Which of the discontinuities are removable? A) no points of discontinuity
B) x = -9 (not removable), x = -5 (removable)
C) x = -9 (removable), x = -5 (not removable)
D) no points of continuity
E) x = -9 (not removable), x = -5 (not removable)
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41
Suppose that and . Find the following limit.
A) -3
B) 5
C) 24
D) -11
E) 0
and . Find the following limit. A) -3
B) 5
C) 24
D) -11
E) 0
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42
Determine the following limit.
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43
Use the rectangles in the graph given below to approximate the area of the region bounded by . Round your answer to three decimal places.
A) 2.481 units2
B) 6.371units2
C) 3.585units2
D) 6.872units2
E) 6.903units2
. Round your answer to three decimal places. A) 2.481 units2
B) 6.371units2
C) 3.585units2
D) 6.872units2
E) 6.903units2
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44
Use the graph as shown to determine the following limits, and discuss the continuity of the function at x= 4.
(i) (ii) (iii)
A) 1, 1, 1, not continuous
B) 2, 2, 2, continuous
C) 1, 1, 1, continuous
D) 2, 2, 2, not continuous
E) 0, 0, 0, not continuous
(i)
(ii) (iii) A) 1, 1, 1, not continuous
B) 2, 2, 2, continuous
C) 1, 1, 1, continuous
D) 2, 2, 2, not continuous
E) 0, 0, 0, not continuous
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45
Find the limit.
A)
B)
C) -12
D) 6
E) 12
A)
B)
C) -12
D) 6
E) 12
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46
Find the limit (if it exists).
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
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47
Find the limit (if it exists).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Suppose that and . Find the following limit.
A) 9
B) -3
C) -21
D) -12
E) 108
and . Find the following limit. A) 9
B) -3
C) -21
D) -12
E) 108
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49
Use the graph as shown to determine the following limits, and discuss the continuity of the function at x= -4.
(i) (ii) (iii)
A) 2, 2, 2, continuous
B) 1, 1, 1, not continuous
C) 2, 2, 2, not continuous
D) -4, -4, -4, continuous
E) 1, 1, 1, continuous
(i)
(ii) (iii) A) 2, 2, 2, continuous
B) 1, 1, 1, not continuous
C) 2, 2, 2, not continuous
D) -4, -4, -4, continuous
E) 1, 1, 1, continuous
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50
Find the x-values (if any) at which is not continuous.
A) f(x) is not continuous at x = -2 and the discontinuity is nonremovable.
B) f(x) is not continuous at x = 0 and the discontinuity is removable.
C) f(x) is continuous for all real x.
D) f(x) is not continuous at x = -2 and the discontinuity is removable.
E) f(x) is not continuous at x = 0, 2 and x = 0 is a removable discontinuity.
is not continuous. A) f(x) is not continuous at x = -2 and the discontinuity is nonremovable.
B) f(x) is not continuous at x = 0 and the discontinuity is removable.
C) f(x) is continuous for all real x.
D) f(x) is not continuous at x = -2 and the discontinuity is removable.
E) f(x) is not continuous at x = 0, 2 and x = 0 is a removable discontinuity.
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51
Find the limit (if it exists).
A)
B)
C) 0
D)
E) Limit does not exist
A)
B)
C) 0
D)
E) Limit does not exist
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52
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Complete the table and use the result to estimate the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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54
Find the value of c guaranteed by the Intermediate Value Theorem.
A) 1
B) 4
C) 6
D) 2
E) 5
A) 1
B) 4
C) 6
D) 2
E) 5
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55
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
A cyclist is riding on a path whose elevation is modeled by the function where x and are measured in miles. Find the rate of change of elevation when x = 3.
A) calculus, 0.72
B) precalculus, 0.12
C) calculus, 0.12
D) precalculus, 0.72
E) precalculus, 0.37
A cyclist is riding on a path whose elevation is modeled by the function
where x and are measured in miles. Find the rate of change of elevation when x = 3.
A) calculus, 0.72
B) precalculus, 0.12
C) calculus, 0.12
D) precalculus, 0.72
E) precalculus, 0.37
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56
Determine the following limit.
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57
Use a graphing utility to graph the function and determine the one-sided limit .
A)
B)
C) 0
D) 3
E) 2
and determine the one-sided limit . A)
B)
C) 0
D) 3
E) 2
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58
Find the x-values (if any) at which the function f(x) = 11x2 - 5x - 5 is not continuous. Which of the discontinuities are removable?
A) x = 2, removable
B) x = 0, removable
C)
D) continuous everywhere
E)
A) x = 2, removable
B) x = 0, removable
C)
D) continuous everywhere
E)
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59
Find the vertical asymptotes (if any) of the function .
A) x = 2
B) x = 6
C) x = -6
D) x = 12
E) x = -2
. A) x = 2
B) x = 6
C) x = -6
D) x = 12
E) x = -2
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60
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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61
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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62
A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places.
A) Radius can vary between 0.91416 inch and 1.09503 inches.
B) Radius can vary between 1.45113 inches and 1.73825 inches.
C) Radius can vary between 0.18475 inch and 2.48475 inches.
D) Radius can vary between 1.58533 inches and 2.07839 inches.
E) Radius can vary between 0.87404 inch and 1.14587 inches.
A) Radius can vary between 0.91416 inch and 1.09503 inches.
B) Radius can vary between 1.45113 inches and 1.73825 inches.
C) Radius can vary between 0.18475 inch and 2.48475 inches.
D) Radius can vary between 1.58533 inches and 2.07839 inches.
E) Radius can vary between 0.87404 inch and 1.14587 inches.
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63
Find the limit (if it exists). Note that represents the greatest integer function.
A) 13
B) Limit does not exist.
C) 12
D) 0
E) 11
represents the greatest integer function. A) 13
B) Limit does not exist.
C) 12
D) 0
E) 11
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64
Let and . Find the limit.
A)
B)
C)
D)
E)
and . Find the limit. A)
B)
C)
D)
E)
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65
Find the constant a such that the function
Is continuous on the entire real line.
A) 1
B) -7
C) 7
D) 14
E) -14
Is continuous on the entire real line.
A) 1
B) -7
C) 7
D) 14
E) -14
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66
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Find the distance traveled in 13 seconds by an object moving with a velocity of feet per second.
A) calculus, 162.3521 ft
B) precalculus, 163.7021 ft
C) calculus, 158.9412 ft
D) precalculus, 158.9412 ft
E) precalculus, 162.3521 ft
Find the distance traveled in 13 seconds by an object moving with a velocity of
feet per second.
A) calculus, 162.3521 ft
B) precalculus, 163.7021 ft
C) calculus, 158.9412 ft
D) precalculus, 158.9412 ft
E) precalculus, 162.3521 ft
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67
Determine the limit (if it exists).
A) 0
B) 56
C) 11
D) 28
E) does not exist
A) 0
B) 56
C) 11
D) 28
E) does not exist
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68
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Find the area of the shaded region.
A) calculus , 15
B) precalculus , 15
C) precalculus , 18
D) calculus , 22
E) precalculus , 22
Find the area of the shaded region.
A) calculus , 15
B) precalculus , 15
C) precalculus , 18
D) calculus , 22
E) precalculus , 22
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69
Use the graph to determine the following limits, and discuss the continuity of the function at x = -4. (i) (ii) (iii)
A) 2, -2, does not exist, not continuous
B) 2, 0, does not exist, not continuous
C) 0, 2, does not exist, not continuous
D) -4, 0, does not exist, not continuous
E) 0, 2, 0, continuous
(ii) (iii) A) 2, -2, does not exist, not continuous
B) 2, 0, does not exist, not continuous
C) 0, 2, does not exist, not continuous
D) -4, 0, does not exist, not continuous
E) 0, 2, 0, continuous
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70
Consider the length of the graph of from to . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places.
A) 7.76
B) 9.77
C) 7.07
D) 9.9
E) 8.76
from to . Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places. A) 7.76
B) 9.77
C) 7.07
D) 9.9
E) 8.76
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71
Find all values of c such that f is continuous on (-∞,∞).
A) c = 2
B) c = 0
C)
D)
E)
A) c = 2
B) c = 0
C)
D)
E)
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72
Find all vertical asymptotes (if any) of the function
A) x = 1, 5
B) x = 1, 5, -4
C) x = -1, -5
D) x = 5
E) x = -5
A) x = 1, 5
B) x = 1, 5, -4
C) x = -1, -5
D) x = 5
E) x = -5
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73
Complete the table and use the result to estimate the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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74
Use the rectangles in the following graph to approximate the area of the region bounded by .
A) 3.9485
B) 2.6323
C) 1.9742
D) 1.4807
E) 0.9871
. A) 3.9485
B) 2.6323
C) 1.9742
D) 1.4807
E) 0.9871
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75
Find the limit (if it exists).
A) 10
B)
C)
D)
E) .
A) 10
B)
C)
D)
E)
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76
Find the limit (if it exists).
A)
B) 0
C) Limit does not exist.
D)
E)
A)
B) 0
C) Limit does not exist.
D)
E)
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77
Let and . Find the limit.
A)
B)
C)
D)
E)
and . Find the limit. A)
B)
C)
D)
E)
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78
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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79
Find all the vertical asymptotes (if any) of the graph of the function .
A) x = -2
B) x = 4
C) x = 0
D) x = 4, x = 0
E) no vertical asymptotes
. A) x = -2
B) x = 4
C) x = 0
D) x = 4, x = 0
E) no vertical asymptotes
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80
A ring has a inner circumference of 2 centimeters. What is the radius of the ring? Round your answer to four decimal places.
A) 0.1592 centimeter
B) 0.6366 centimeter
C) 0.3183 centimeter
D) 0.7979 centimeter
E) 0.4053 centimeter
A) 0.1592 centimeter
B) 0.6366 centimeter
C) 0.3183 centimeter
D) 0.7979 centimeter
E) 0.4053 centimeter
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