Exercises 25 – 30, use the Taylor series given in Key Idea 32 to create the Taylor series of the given func??ons.
\(f(x) = cos (x^2)\)
Key Idea 32 informs us that:
\(cos(x) = \sum_{\infty }^{n=0}(-1)^{n}\frac{x^{2n}}{(2n)!}\)
\(= 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + ....\)
\(cos(x^2) = \sum_{\infty }^{n=0}(-1)^{n}\frac{(x^2)^{2n}}{(2n)!}\)
\(= 1 - \frac{x^4}{2!} + \frac{x^8}{4!} - \frac{x^12}{6!} + ....\)