Question

1. Differentiate the given series expansion of ff term-by-term to obtain the corresponding series expansion for...

1. Differentiate the given series expansion of ff term-by-term to obtain the corresponding series expansion for the derivative of f .

If f(x)= x^3/1−x = ∞∑n=0 x^3+n
f'(x)= ∞∑n=0 =

2. Integrate the given series expansion of ff term-by-term from zero to xx to obtain the corresponding series expansion for the indefinite integral of ff.

If f(x)= 4x^3 /1+x^4 = ∞∑n=0 (−1)^n 4x^4n+3
∫ 0 to x f(t)dt = ∞∑n=0 =

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