Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is not.
Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is not.
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:Show that the function f(t) = sin(e*) is of exponential
order as t → +oo but that its derivative is not.
Expert Solution
Step 1
To show that the given function is of exponential order.
Step 2
Given
In order to check the exponential function, we check if the where is a positive constant.
If this equals to zero, then the function is of exponential order.
Since the term in numerator i.e. has value at-most 1 because that is the range of sine function.
Thus, we choose the value of so that
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