Question

How do you find the first two nonzero terms in Maclaurin's Formula and use it to approximate `f(1/3)` given `f(x)=sqrt(x^2+1)`?

Answer 1

Please see the explanation below

Explanation:

The expansion is

`f(x)=sqrt(1+x^2)=1+x^2/2+.....`

Therefore,

`f(1/3)=sqrt(1+1/9)=sqrt10/3=1.054`

`f(1/3)=1+(1/3)^2/2=1+1/18=19/18=1.056`