Question

find the first four nonzero terms for the taylor series about 0, for \[f(x)=\sqrt{(1+x)}\cos(2x)\]

Answer 1

Taylor series about 0 is same as maclaurin series :
\[f(x) = \sum_{k=0}^{\infty} \frac{f^k(0)}{k!} x^k\]

Answer 2

find the derivatives and plugin

Answer 3

i am having trouble combinding the third and fourth terms @ganeshie8 the first two i got were 1 and x/2

Answer 4

thats a good start !

Answer 5

the higher derivatives look a bit ugly
see if this helps
http://www.wolframalpha.com/input/?i=taylor+series+sqrt%281%2Bx%29*cos%282x%29