Proving Pn(x^2) as the 4n+2-nd Taylor Polynomial of sin(x^2) using Rn(x) Limits

[trap]

Show that Pn(x^2) is the 4n+2-nd Taylor polynomial of sin(x^2) by showing that
\lim_{n\rightarrow infinity} R2n+1(x^2) = 0.

note that Rn(x) represents the remainder

I'm stuck on this question, can anyone help me please?

 

[Hurkyl]

On what are you stuck? Do you know what P_n(x^2) is? Do you know what R_2n+1(x^2) is? Do you know how to prove its limit goes to zero? Do you know why that limit would imply what you're trying to prove?

 

[trap]

I'm stuck on the entire question, I know what P and R are but i don't know how to prove the question. I also do not know why the limit of R helps solve this question.