Chapter 8: Q. 52 (page 692)

Find the Maclaurin series for the functions in Exercises 51–60 by substituting into a known Maclaurin.
Also, give the interval of convergence for the series.
$e^{- 3 x^{2}}$

Short Answer

Expert verified

The required Maclaurin series is $e^{- 3 x^{2}} = \sum_{k = 0}^{\infty} \frac{(- 3)^{k} x^{2 k}}{k!}$

Step by step solution

Step 1. Given Information

Consider the function $f (x) = e^{- 3 x^{2}}$

Step 2

We know that the Maclaurin series for the function $g (x) = e^{x}$ is $e^{x} = \sum_{k = 0}^{\infty} \frac{x^{k}}{k!}$

So, to find the Maclaurin series of the function $f (x) = e^{- 3 x^{2}}$ , we replace $x$ by $- 3 x^{2}$ in the Maclaurin series of the function $e^{x}$

Therefore, $e^{- 3 x^{2}} = \sum_{k = 0}^{\infty} \frac{{(- 3 x^{2})}^{k}}{k!}$ implies that $e^{- 3 x^{2}} = \sum_{k = 0}^{\infty} \frac{(- 3)^{k} x^{2 k}}{k!}$

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Find the Maclaurin series for the functions in Exercises 51–60 by substituting into a known Maclaurin.
Also, give the interval of convergence for the series.
$e^{- 3 x^{2}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2

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Find the Maclaurin series for the functions in Exercises 51–60 by substituting into a known Maclaurin.Also, give the interval of convergence for the series.e-3x2

Short Answer

Step by step solution

Step 1. Given Information

Step 2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Applied Mathematics

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Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find the Maclaurin series for the functions in Exercises 51–60 by substituting into a known Maclaurin.
Also, give the interval of convergence for the series.
$e^{- 3 x^{2}}$