Chapter 1.

1.1 Problem Statement

{6,7,8}
$a*$a+1
$a*$a
round(-0.5*pow($aa,-3/2),6)
round(1/sqrt($a1)-1/$a,6)
round(abs($df - $ans1),6)

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

1.2 Step 1

Question Sequence

Question 1.1

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

Δf ≈ UM+zqoEu/CzVEMfD3LkDwsAhMucu5VsNDQG5PghLPy0=,

where the exact value of Δf is

Δf = f(a + Δx) - f(a).

Correct.
Incorrect.

Question 1.2

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

f(x) = with a =jheSL/qS2j8= and Δx =0VV1JcqyBrI=.

Correct.
Incorrect.

1.3 Step 2

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

Question Sequence

Question 1.3

Find f'(x) and f'($aa).

f'($aa) = UFPfACDOxzX9rlDg

Correct.
Incorrect.

Question 1.4

Approximate Δf using the Linear Approximation.

Δf ≈ f'($aa)Δx = UFPfACDOxzX9rlDg

Correct.
Incorrect.

1.4 Step 3

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

Question Sequence

Question 1.5

Δf = lkh6vxty4QM=

Correct.
Incorrect.

Question 1.6

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

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

|Δf - f'($aa)Δx| = ttsddHJTLg4=

Correct.
Incorrect.