error estimate for sqrt[1 + x] = 1 + x/2 for |x| < 0.1

[cheffy]

The estimate \(\displaystyle \
\sqrt {1 + x} = 1 + \frac{x}{2}
\\)
is used when x is small. Estimate the error when |x|<0.1

I know it has something to do with |-(x^2)/8|, at least I think, but I don't know what to do from here. Thanks!

 

[galactus]

Try the Taylor series:

\(\displaystyle \L\\\sqrt{1+x}=1+\frac{x^{2}}{2}-\frac{x^{2}}{8}+...........\)

\(\displaystyle \L\\1+\frac{1}{x}=1+\frac{x}{2}\)

 

[cheffy]

What am I supposed to do with that?

I don't understand how you got the second line.