Find the first few terms of the Maclaurin series for each of the following functions and check your results by computer. 20. \( e^{x} \sin x \) 21. \( \tan ^{2} x \) 22. \( \frac{e^{x}}{1-x} \)
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\( e^{x} \sin x \) The Maclaurin series for \( e^{x} \) is \( 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \cdots \) The Maclaurin series for \( \sin x \) is \( x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + \cdots Show more…
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