1+ 5. Suppose g(x) = p. The Maclaurin series for g is 1 - x + x - x +...+(-1)"x3* + ..., which converges to g(x) for Ixl

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1 5 Suppose G X P The Maclaurin Series For G Is 1 X X X 1 X3 Which Converges To G X For Ixl 1 (34.09 KiB) Viewed 21 times

1+ 5. Suppose g(x) = p. The Maclaurin series for g is 1 - x + x - x +...+(-1)"x3* + ..., which converges to g(x) for Ixl < 1. (a) Write the first three nonzero terms and the general term of the Maclaurin scries for g'(x). fce) flex.c)+ f '(c) ex-c) ² . f"ce '2 2 *** (b) Using your answer to part (a), find the sum of the infinite series + 3n +(-1)" 23-1 (c) Write the first four nonzero terms and the general term of the Maclaurin series for Sg(t)dt. (d) Using the first three nonzero terms of your answer to part (C), approximate S'? 9(t) dt. Use the Alternating Series Remainder to show that this approximation is guaranteed to be within of the exact value of Sg(t) dt. 1 10,000