Consider the limit L and the integral I defined by 1 - lim (2²+ 3+1) L = 118 (a) Use L'Hôptial's Rule to evaluate the limit L (b) Explain why the integral I is improper. (c) Evaluate I. and I = 8 [ 0 0 d. 4x²e-2x
Consider the limit L and the integral I defined by 1 - lim (2²+ 3+1) L = 118 (a) Use L'Hôptial's Rule to evaluate the limit L (b) Explain why the integral I is improper. (c) Evaluate I. and I = 8 [ 0 0 d. 4x²e-2x
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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Transcribed Image Text:Consider the limit L and the integral I defined by
L lim
1→∞
=
(a) Use L'Hôptial's Rule to evaluate the limit L
(b) Explain why the integral I is improper.
(c) Evaluate I.
2t² + 2t + 1
e²t
= 1.°
and I =
4x²e-²x dx
Expert Solution
Step 1
The given limit is
The given limit is of the form .
Apply L'Hospital rule, Calculate the derivative of numerator and denominator separately.
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