# Thread: Linear Approximation and Error Problem

1. ## Linear Approximation and Error Problem

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

2. Originally Posted by Quiz0n
Estimate the quantity using Linear Approximation and find the error using a calculator.

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

So:

$\displaystyle \frac{1}{\sqrt{98}}-\frac{1}{\sqrt{95}} \approx -(1/2)(3/95^{1.5}) + R/\sqrt{95}$

RonL

3. I need in a numerical form, I got the answer -0.0015 using examples from my textbook, but it's apparently incorrect. Thanks for the help. I still can't figure it out.

4. Originally Posted by Quiz0n
I need in a numerical form, I got the answer -0.0015 using examples from my textbook, but it's apparently incorrect. Thanks for the help. I still can't figure it out.
You have a calculator, so you can evaluate what I gave in my earlier post.

If you are going to give an answer to two significant digits round it correctly
don't just truncate the answer to two significant digits.

RonL