Estimate the quantity using Linear Approximation and find the error using a calculator.
I need the and the error in Linear Approximation, please help!
Look at the first term:
$\displaystyle
\frac{1}{\sqrt{95+3}}= \frac{1}{\sqrt{95}}\frac{1}{\sqrt{1+3/95}}
$
..... $\displaystyle = \frac{1}{\sqrt{95}} [1-(1/2)(3/95) + R]$
where $\displaystyle R \approx (3/8)(3/95)^2$ is the remainder, or the error in the linear approximation.
(here I am using a rule of thumb that the error is approximatly the first neglected term, in this case
this can be made precise)
So:
$\displaystyle
\frac{1}{\sqrt{98}}-\frac{1}{\sqrt{95}} \approx -(1/2)(3/95^{1.5}) + R/\sqrt{95}
$
RonL