Math  /  Calculus

QuestionFind the Taylor series about 0 for each of the functions below. Give the first three nonzero terms for each. A. x2sin(x2)x4=x^{2} \sin \left(x^{2}\right)-x^{4}= \square ++ \square \square ++ ++\cdots B. 2cos(x)+x2=2 \cos (x)+x^{2}= \square ++ \square ++ \square ++\cdots
For each of these series, also be sure that you can find the general term in the series!

Studdy Solution
A. x2sin(x2)x4=x86+x12120x165040+x^2 \sin(x^2) - x^4 = -\frac{x^8}{6} + \frac{x^{12}}{120} - \frac{x^{16}}{5040} + \dots B. 2cos(x)+x2=2+x412x6360+2 \cos(x) + x^2 = 2 + \frac{x^4}{12} - \frac{x^6}{360} + \dots

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