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Find the first four nonzero terms in the Maclaurin series for the functions.$$e^{x} \sin x$$
$x+x^{2}+\frac{x^{3}}{3}-\frac{x^{5}}{30}+\cdots$
Calculus 2 / BC
Chapter 9
Infinite Sequences and Series
Section 9
Convergence of Taylor Series
Sequences
Series
Missouri State University
Campbell University
University of Michigan - Ann Arbor
Idaho State University
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first, we need to remember to tailor Siri's expressions, and I'm going to write the 1st 4 terms of these expressions Now, in order to figure out the 1st 4 terms of the tailor, Siri's expended about zero for each of the X sign of X. All we're going to do is foil E to the EC, the Taylor series for E to the X and the Taylor series for a sign of X. And we're going to do this carefully, paying attention to the powers of the terms so one times x is x x times X is X squared. We get X cubed, divided by two minus X cubed, divided by three factorial plus X to the fore, divided by six minus X to the fore, divided by two times three factorial and then dot, dot dot Let's go ahead and simplify, and then finally, we consider the fire fractions a little bit more. So let's see. This is 3/6, so that gives us to over six or 1/3. And here we're just going to have 1/12 extra before
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