Consider the following piecewise-defined function: 2, tIn4 (a) Sketch the graph of f(t) and clearly mark all points where the character of the function changes. (b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of this linear combination may be functions of t. (c) Calculate the Laplace transform £{f}.

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.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Consider the following piecewise-defined function:
2,
t<ln 2
f(t)=
=
et
In 2<t<ln 4
+2,
t>In4
(a) Sketch the graph of f(t) and clearly mark all points where the character of the function
changes.
(b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of
this linear combination may be functions of t.
(c) Calculate the Laplace transform £{f}.
Transcribed Image Text:Consider the following piecewise-defined function: 2, t<ln 2 f(t)= = et In 2<t<ln 4 +2, t>In4 (a) Sketch the graph of f(t) and clearly mark all points where the character of the function changes. (b) Express f(t) as a linear combination of shifted Heaviside functions. The coefficients of this linear combination may be functions of t. (c) Calculate the Laplace transform £{f}.
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