Use the table of Maclaurin series to find the first few terms of the Maclaurin series...

 

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Use the table of Maclaurin series to find the first few terms of the Maclaurin series of f(x) = sin(x²). b) Use this series to find the first few terms of the series for sin(x²) dx. c) What is the minimum number of terms of the series found in part b) necessary to approximate the integral so that lerror] < 10-4? Approximate the integral with that number of terms. d) Is the approximation in part c) too large or too small? Why? e) Use the Alternating series Remainder Theorem to find an upper bound for the lerror] of the approximation found in part c). Use the table of Maclaurin series to find the first few terms of the Maclaurin series of f(x) = sin(x²). b) Use this series to find the first few terms of the series for sin(x²) dx. c) What is the minimum number of terms of the series found in part b) necessary to approximate the integral so that lerror] < 10-4? Approximate the integral with that number of terms. d) Is the approximation in part c) too large or too small? Why? e) Use the Alternating series Remainder Theorem to find an upper bound for the lerror] of the approximation found in part c). Use the table of Maclaurin series to find the first few terms of the Maclaurin series of f(x) = sin(x²). b) Use this series to find the first few terms of the series for sin(x²) dx. c) What is the minimum number of terms of the series found in part b) necessary to approximate the integral so that lerror] < 10-4? Approximate the integral with that number of terms. d) Is the approximation in part c) too large or too small? Why? e) Use the Alternating series Remainder Theorem to find an upper bound for the lerror] of the approximation found in part c).