Find the Taylor polynomial of degree 4 forcosx forxnear 0 P4

Find the Taylor polynomial of degree 4 forcos(x), forxnear 0:
P4(x)=

SOLVE THE FOLLOWING

Approximatecos(x)withP4(x)to simplify the ratio:
x1?cos(x)=

Solution

(1-cos(x))/x=x/2-x^3/24