What is the Maclaurin series for f(x)=sin(x2)f(x) = \sin(x^2)f(x)=sin(x2)?
∑n=0∞(−1)nx4n+2(2n+1)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{4n+2}}{(2n+1)!}∑n=0∞(−1)n(2n+1)!x4n+2
∑n=0∞(−1)nx2n(2n+1)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n}}{(2n+1)!}∑n=0∞(−1)n(2n+1)!x2n
∑n=0∞x4n+2(2n+1)!\sum_{n=0}^{\infty} \frac{x^{4n+2}}{(2n+1)!}∑n=0∞(2n+1)!x4n+2
∑n=0∞(−1)nx2n+2(2n+1)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+2}}{(2n+1)!}∑n=0∞(−1)n(2n+1)!x2n+2