Question

Only C and D are necessary.

An approximation attributed to both James Gregory (1638-1675) and Goltfried Leibniz (1646-1716) relies 1. tan +.", for-1 <xs 1. on the Taylor series for the inverse tangent (Sectlon 9.3): 3 S 7 a. Substitute x 1 into the Taylor series and write out a series that converges lo a/4. b. Write the first ten terms of the sequence of partial sums for the series. What is the error in the approximation to x/4 using ten terms? (Assume a calculator gives the "exact" value of x.) c. Use the Remainder in Alternating Series Theorem to estimate the error introduced when the series is terminated after 100 terms. d. How many terms of this series must be used to oblain an 1062 approximation to n with an error no greater than

Answer 1

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