For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such as geometric series, binomial series, or the Maclaurin...

Can I please get the answers for b and c?

Extracted text: For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such as geometric series, binomial series, or the Maclaurin series for e*, sin x, arctan x, and ln(1 +x). (a) If f(x) = (1+x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f (x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! flm)(a) = (а-1)"(п + 1)" show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than 0.0002.