Problem

Find the first three nonzero terms of the Maclaur…

Problem 3 Easy Difficulty

Find the first three nonzero terms of the Maclaurin expansion of the given functions.
$$f(x)=e^{x}$$

Answer

$1+\frac{1}{1 !} x+\frac{1}{2 !} x^{2}+\frac{1}{3 !} x^{3}$

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Calculus 2 / BC

Basic Technical Mathematics with Calculus

Chapter 30

Expansion of Functions in Series

Section 2

Mclaurin Series

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Video Transcript

we want to find the first three non zero terms of the MacLaurin series. For the function affects equal to E V X. His question is challenge your understanding of series and of series expansions. Remember that MacLaurin series is of the form for fx adam zero plus time of zero X plus F double prime 0/2 factorial X squared plus F three, 0/3 factorial X cube. That is, it is the sum of every derivative of F zero divided by n factorial times X to the end. So we see that to find MacLaurin series for fx we're gonna need to find the derivatives and evaluate zero. So the directives are E G expressed one of the extra F to E, the extra three and so on. Because they are the X is always itself. We always have it all F n r E to the X. Therefore because even the zero is one all of our F F prime eligible crime and so on. Of zero or one. And we must have our series given us one plus X plus one half X squared expanding

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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