
Linear Approximation
Estimate the quantity using Linear Approximation and find the error using a calculator.
https://webwork.math.lsu.edu/webwork...7a371a6c81.png
The Linear Approximation is: https://webwork.math.lsu.edu/webwork...27536bf091.png
The error in Linear Approximation is:
I know that:
$\displaystyle
f(x) = 1/(sqrtx)
, a=95
$ and the change in x is 4.
So:
f'(x)=1/2(x)^(3/2)
f'(a)=1/2(1/95)^(3/2)
f'(a)=.000539988606
Change in F=f'(a)*Change in x
So:
delta f=(4)*(.000539988606)
delta f=.0021599544
Actual change=f(a+delta x)f(a)
=f(95+4)f(95)
=.0020940537
Error in Approximation= absolute value of (delta f  actual change)
= (.0021599544(.0020940537))
=.000065900717
**Updated with right answers for those that may need help.**

Solved the problem. Updated original post for those that may need help in the future.