Proposition in taylor polynomials?

Question

How do i use proposition to find the 4th degree polynomial (p4(n)) of f(x)= e^(x^2)

Answer 1

i understand your question to mean find the taylor polynomial of exp(x^2) to the fourth power of x

first write out the taylor expansion of exp(x):

exp(x)=1+x+x^2/2! +x^3/3!+x^4/4!

now, substitute x^2 for each x and get:

exp(x^2)=1+x^2+x^4/2!+x^6/3!+x^8/4!+.....