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Polynomial graphs

### Describe any similarities and differences. Refer to the end behaviour, local maximum and local minimum points, and maximum and minimum points. a) Sketch graphs of $$\displaystyle{y}={\sin{\ }}{x}$$ and $$\displaystyle{y}={\cos{\ }}{x}.$$ b) Compare the graph of a periodic function to the graph of a polynomial function.

Polynomial graphs

### 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.

Polynomial graphs

### (a) find the Maclaurin polynomial $$\displaystyle{P}_{{{3}}}{\left({x}\right)}$$ for PSKf(x), (b) complete the following PSKx: -0.75, -0.50, -0.25, 0, 0.25, 0.50, 0.75 for f(x) and P_{3}(x) and (c) sketch the graphs of f(x) and $$\displaystyle{P}_{{{3}}}{\left({x}\right)}$$ on the same set of coordinate axes. $$\displaystyle{f{{\left({x}\right)}}}={\arctan{{x}}}$$

Polynomial graphs