Problem Statement

{6,7,8}
6*6+1
6*6
round(-0.5*pow(36,-3/2),6)
round(1/sqrt(37)-1/6,6)
round(abs(-0.002268 - -0.002315),6)

Estimate using the Linear Approximation and find the error using a calculator.

 
Step 1

Question Sequence

Question 1

If the function f is differentiable at x = a and Δx is small, then the Linear Approximation of Δf is

Δf ≈ ,

where the exact value of Δf is

Δf = f(a + Δx) - f(a).

Correct.
Incorrect.

Question 2

By rewriting as , it is apparent the Linear Approximation should be applied to the function

f(x) = with a = and Δx =.

Correct.
Incorrect.

 
Step 2

To approximate Δf, we need to compute f'(36)Δx. (Round your answers to six decimal places.)

Question Sequence

Question 3

Find f'(x) and f'(36).

f'(36) =

Correct.
Incorrect.

Question 4

Approximate Δf using the Linear Approximation.

Δf ≈ f'(36)Δx =

Correct.
Incorrect.

 
Step 3

Using a calculator, estimate the actual change, Δf = , to six decimal places.

Question Sequence

Question 5

Δf =

Correct.
Incorrect.

Question 6

The error in the Linear Approximation is the quantity |Δf - f'(36)Δx|.

Calculate the error in the Linear Approximation. (Round your answer to six decimal places.)

|Δf - f'(36)Δx| =

Correct.
Incorrect.