Using calculus, it can be shown that the tangent function can be approximated by the polynomial tan x approx x + frac{2x^{3}}{3!} + frac{16x^{5}}{5!} where x is in radians. Use a graphing utility to graph the tangent function and its polynomial approximation in the same viewing window. How do the graphs.

Using calculus, it can be shown that the tangent function can be approximated by the polynomial tan x approx x + frac{2x^{3}}{3!} + frac{16x^{5}}{5!} where x is in radians. Use a graphing utility to graph the tangent function and its polynomial approximation in the same viewing window. How do the graphs.

Question
Polynomial graphs
asked 2021-02-15
Using calculus, it can be shown that the tangent function can be approximated by the polynomial \(\displaystyle{\tan{\ }}{x}\ \approx\ {x}\ +\ {\frac{{{2}{x}^{{{3}}}}}{{{3}!}}}\ +\ {\frac{{{16}{x}^{{{5}}}}}{{{5}!}}}\) where x is in radians. Use a graphing utility to graph the tangent function and its polynomial approximation in the same viewing window. How do the graphs.

Answers (1)

2021-02-16
The red graph is tangent and the blue graph is approximation. The graphs aresimilar close to when \(\displaystyle{x}={0}\). image
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