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2 (a) () Page 3 of 11 Using the power series expansion for exp(-x) or otherwise, find the first 3 non-zero terms in the power series expansion of exp(-2x¹). Remember that exp(-x) is the same as e Module code: CAPE200001 (ii) Use the power series from (i) to find the limit of (ii) Calculate lim 140 1-exp(-2x²) Turn the page over 1-2r²-exp(-2r²) using l'Hôpital's rule. as x-0.

2 (a) () Page 3 of 11 Using the power series expansion for exp(-x) or otherwise, find the first 3 non-zero terms in the power series expansion of exp(-2x¹). Remember that exp(-x) is the same as e Module code: CAPE200001 (ii) Use the power series from (i) to find the limit of (ii) Calculate lim 140 1-exp(-2x²) Turn the page over 1-2r²-exp(-2r²) using l'Hôpital's rule. as x-0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2 (a) Page 3 of 11 (0) Module code: CAPE200001 (ii) (ii) Using the power series expansion for exp(-x) or otherwise, find the first 3 non-zero terms in the power series expansion of exp(-2x¹). Remember that exp(-x) is the same as e. Calculate lim Use the power series from (i) to find the limit of 1-2²-e 1-exp(-2x¹) Turn the page over using l'Hôpital's rule. 2²-exp(-2²) as x→0.
Transcribed Image Text:2 (a) Page 3 of 11 (0) Module code: CAPE200001 (ii) (ii) Using the power series expansion for exp(-x) or otherwise, find the first 3 non-zero terms in the power series expansion of exp(-2x¹). Remember that exp(-x) is the same as e. Calculate lim Use the power series from (i) to find the limit of 1-2²-e 1-exp(-2x¹) Turn the page over using l'Hôpital's rule. 2²-exp(-2²) as x→0.
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