In calculus, it can be shown that the arctangent function can be approximated by the polynomial arctan x approx x-x^{3}/3+x^{5}/5-x^{7}/7 where x is in radians. Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare?

In calculus, it can be shown that the arctangent function can be approximated by the polynomial arctan x approx x-x^{3}/3+x^{5}/5-x^{7}/7 where x is in radians. Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare?

Question
Polynomial graphs
asked 2021-02-25
In calculus, it can be shown that the arctangent function can be approximated by the polynomial
\(\displaystyle{\arctan{{x}}}\approx{x}-\frac{{x}^{{{3}}}}{{3}}+\frac{{x}^{{{5}}}}{{5}}-\frac{{x}^{{{7}}}}{{7}}\)
where x is in radians. Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare?

Answers (1)

2021-02-26

Step 1
The red graph is arctanx and the blue graph is the approximation. They are similar close to the origin.
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