# How do you find the first five terms of the Taylor series for #f(x)=x^8+x^4+3# at #x=1#?

##### 1 Answer

Mar 1, 2015

The Taylor series is a particular way to approximate a function with a polynomial in the neighbourhood of a generic point

or, with the series notation:

So, let's calculate all the derivatives we need:

so:

It's easy to understand that if you would calculate the Taylor's series until the 8th order you will obtain the function itself, because it is a polynomial!