Show that the Maclaurin series for 2e− x2√4 − x2is 1 −x2+x24+ · · ·.Hence,i. evaluate limx→02e− x2√4 − x2− 1x.ii. approximate the definite integral Z 0.40.12e− x2x√4 − x2dx correct to 4 decimalplaces. 2e-is 1x2+...Show that the Maclaurin series forV4 – x2Hence,2e-1VA – x²i. evaluate lim2e-ii, approximate the definite integral Jo1 rV4 – x²c0.4dx correct to 4 decimalplaces.8 IN

Answered: Image /qna-images/answer/fe3f809d-5572-4209-87d5-6be8879d5690.jpg

Answered: 2e- 1 V4 – x² i. evaluate lim c0.4 2e-를…

2e- 1 V4 – x² i. evaluate lim c0.4 2e-를 ii. approximate the definite integral / dx correct to 4 decimal x/4 – x2 places.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 49RE

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Question

Show that the Maclaurin series for 2e
− x
2
√
4 − x
2
is 1 −
x
2
+
x
2
4
+ · · ·.

Hence,
i. evaluate limx→0
2e
− x
2
√
4 − x
2
− 1
x
.

ii. approximate the definite integral Z 0.4
0.1
2e
− x
2
x
√
4 − x
2
dx correct to 4 decimal
places.