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1. Find the convolution of (a) 2tu(t) and t³u(t) (b) e¹u(t) and tu(t) (c) e¯²tu(t) and e¯tu(t). In each case reverse the order to check that (f * g)(t) = (g* f)(t). Answers 1. (a) 11/05 (b) -t-1+et (c) e−t — e−2

1. Find the convolution of (a) 2tu(t) and t³u(t) (b) e¹u(t) and tu(t) (c) e¯²tu(t) and e¯tu(t). In each case reverse the order to check that (f * g)(t) = (g* f)(t). Answers 1. (a) 11/05 (b) -t-1+et (c) e−t — e−2

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 25E
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1. Find the convolution of (a) 2tu(t) and t³u(t) (b) etu(t) and tu(t) (c) e−2u(t) and e¯tu(t). In each case reverse the order to check that (ƒ * g)(t) = (g* f)(t). Answers 1. (a) 1/1 +5 (b)-t-1+et (b)-t-1+et (c) e-te-2
Transcribed Image Text:1. Find the convolution of (a) 2tu(t) and t³u(t) (b) etu(t) and tu(t) (c) e−2u(t) and e¯tu(t). In each case reverse the order to check that (ƒ * g)(t) = (g* f)(t). Answers 1. (a) 1/1 +5 (b)-t-1+et (b)-t-1+et (c) e-te-2
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