Question 1

Use Newton's method to approximate the given number correct to eight decimal places 
A) 
B) 
C) 
D) 
E)

Accepted Answer

C

Question 2

The sum of two positive numbers is 16.What is the smallest possible value of the sum of their squares?

Accepted Answer

128

Question 3

Find f, 
A) 
B) 
C) 
D) 
E) None of these

Accepted Answer

C

Question 4

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) 6
B) 1
C) 12
D) 11
E) 0

Accepted Answer

The answer of Given that the graph of f passes...

Question 5

Find the position function of a particle moving along a coordinate line that satisfies the given condition.  ,s(1) = -1

Accepted Answer

The answer of Find the position function of a particle...

Question 6

A particle is moving with the given data.Find the position of the  , 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A particle is moving with the given...

Question 7

Find the most general antiderivative of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the most general antiderivative of the...

Question 8

Find two positive numbers whose product is 121 and whose sum is a minimum.
A) 6,24
B) 2,72
C) 4,36
D) 11,11
E) 3,48

Accepted Answer

We can write the given number as $11eaae29\_f512\_bf7a\_87fe\_c7da465412f4\_TB2067\_11=11	imes10^{16}+eaae29\_f512\_bf7a\_87fe\_c7da465412f4\_TB2067\_11$. Let the two numbers be $x$ and $y$. We want to minimize $x+y$. By AM-GM inequality,
$$x+y\geq2\sqrt{xy}=2\sqrt{(11	imes10^{16}+eaae29\_f512\_bf7a\_87fe\_c7da465412f4\_TB2067\_11)}.$$ 
Now it is enough to minimize $11	imes10^{16}+eaae29\_f512\_bf7a\_87fe\_c7da465412f4\_TB2067\_11$ which is greater than $11	imes10^{16}$. Therefore, $x+y$ is minimized when $x=y=\sqrt{11	imes10^{16}+eaae29\_f512\_bf7a\_87fe\_c7da465412f4\_TB2067\_11}/2$. Hence the answer is D.

Question 9

A woman at a point A on the shore of a circular lake with radius 4 mi 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 6 mi/h and row a boat at 2 mi/h .How should she proceed? (Find  ).Round the result,if necessary,to the nearest hundredth. 
A) 0.44 radians
B) She should walk around the lake from point A to point C.
C) 0.46 radians
D) She should row from point A to point C radians
E) 0.62 radians

Accepted Answer

The answer of A woman at a point A on...

Question 10

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.)

Accepted Answer

The answer of Use Newton's method with the specified initial...

Question 11

What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in 4 s?

Accepted Answer

The answer of What constant acceleration is required to increase...

Question 12

Use Newton's method with the specified initial approximation  to find  ,the third approximation to the root of the given equation.(Round your answer to four decimal places.) 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Using Newton's method with initial approximation 11eaae29_f50f_15dd_87fe_f168c4020f30_TB2067_11, we compute:

f(11eaae29_f50f_15dd_87fe_f168c4020f30_TB2067_11) = -3.1453
f'(11eaae29_f50f_15dd_87fe_f168c4020f30_TB2067_11) = 16.4354
11eaae29_f50f_15dd_87fe_f168c4020f30_TB2067_11 - (-3.1453)/16.4354 = 11eaae29_f50f_3cef_87fe_39ea5305c01c_TB2067_11

Round to four decimal places to get 11eaae29_f50f_b223_87fe_dd1e4ab92493_TB2067_11 as the third approximation. Therefore, the answer is D.

Question 13

Find f, 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find f, 
A) 
B) 
C) 
D) 
E)...

Question 14

Find the position function of a particle moving along a coordinate line that satisfies the given conditions.  ,s (0)= 5,v (0)= 0

Accepted Answer

The answer of Find the position function of a particle...

Question 15

Find the most general antiderivative of the function.

Accepted Answer

The answer of Find the most general antiderivative of the...

Question 16

Find the point on the line  that is closest to the origin.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the point on the line ...

Question 17

A car braked with a constant deceleration of 40  ,producing skid marks measuring 60 ft before coming to a stop.How fast was the car traveling when the brakes were first applied?

Accepted Answer

The answer of A car braked with a constant deceleration...

Question 18

Use Newton's method with the specified initial approximation  to find  ,the third approximation to the root of the given equation.(Round your answer to four decimal places.) 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use Newton's method with the specified initial...

Question 19

Find the most general antiderivative of the function.

Accepted Answer

The answer of Find the most general antiderivative of the...

Question 20

Use Newton's method to approximate the indicated root of  in the interval  ,correct to six decimal places.
Use  as the initial approximation.

Accepted Answer

The answer of Use Newton's method to approximate the indicated...

Quiz 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Use Newton's method to approximate the given number correct to eight decimal places

The sum of two positive numbers is 16.What is the smallest possible value of the sum of their squares?

Find f,

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) .

Find the position function of a particle moving along a coordinate line that satisfies the given condition. ,s(1) = -1

A particle is moving with the given data.Find the position of the particle ,

Find the most general antiderivative of the function.

Find two positive numbers whose product is 121 and whose sum is a minimum.

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.)

What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in 4 s?

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Round your answer to four decimal places.)

Find f,

Find the position function of a particle moving along a coordinate line that satisfies the given conditions. ,s (0)= 5,v (0)= 0

Find the most general antiderivative of the function.

Find the point on the line that is closest to the origin.

A car braked with a constant deceleration of 40 ,producing skid marks measuring 60 ft before coming to a stop.How fast was the car traveling when the brakes were first applied?

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Round your answer to four decimal places.)

Find the most general antiderivative of the function.

Use Newton's method to approximate the indicated root of in the interval ,correct to six decimal places. Use as the initial approximation.