# Linear Approximation and Error Problem

• Oct 9th 2007, 11:11 AM
Quiz0n
Linear Approximation and Error Problem
Estimate the quantity using Linear Approximation and find the error using a calculator.

https://webwork.math.lsu.edu/webwork...a613bb9f71.png

• Oct 9th 2007, 12:06 PM
CaptainBlack
Quote:

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

https://webwork.math.lsu.edu/webwork...a613bb9f71.png

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
• Oct 9th 2007, 12:32 PM
Quiz0n
I need https://webwork.math.lsu.edu/webwork...27536bf091.png 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.
• Oct 9th 2007, 08:30 PM
CaptainBlack
Quote:

Originally Posted by Quiz0n
I need https://webwork.math.lsu.edu/webwork...27536bf091.png 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