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

The Linear Approximation is:

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.**