| 14. Polynomial Approximation Using calculus, it can be shown that the arctangent function can be approximated by the polynomial arctan x = x 3 5 7 where x is in radians. (a) Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare? (b) Study the pattern in the polynomial approximation of the arctangent function and predict the next term. Then repeat part (a). How does the accuracy of the approximation change when an additional term is added?
| 14. Polynomial Approximation Using calculus, it can be shown that the arctangent function can be approximated by the polynomial arctan x = x 3 5 7 where x is in radians. (a) Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare? (b) Study the pattern in the polynomial approximation of the arctangent function and predict the next term. Then repeat part (a). How does the accuracy of the approximation change when an additional term is added?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section: Chapter Questions
Problem 14PS
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Question
Polynomial Approximation Using calculus, it
can be shown that the arctangent
approximated by the polynomial
arctan x ≈ x − x3
3
+
x5
5 − x7
7
where x is in radians.
(a) Use a graphing utility to graph the arctangent
function and its polynomial approximation in
the same viewing window. How do the graphs
compare?
(b) Study the pattern in the polynomial approximation
of the arctangent function and predict the next term.
Then repeat part (a). How does the accuracy of the
approximation change when an additional term is
added?
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