| eat cos(bt) dt = eat a cos(bt) + b sin(bt) + C. a2 + 62 a. Use this antiderivative to compute the following improper integral: lim TH00 e4t cos (3t) e st dt = if s + 4 or -st dt et cos(3t) e Jo lim sin(3T)/3 T00 if s = 4. he (formulas)
| eat cos(bt) dt = eat a cos(bt) + b sin(bt) + C. a2 + 62 a. Use this antiderivative to compute the following improper integral: lim TH00 e4t cos (3t) e st dt = if s + 4 or -st dt et cos(3t) e Jo lim sin(3T)/3 T00 if s = 4. he (formulas)
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.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 45E
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I am having trouble finding a solution to the equation in part a and part c.
![eat
cos(bt) dt =
a cos(bt) + b sin(bt)
+ C.
eat
a2 + 62
a. Use this antiderivative to compute the following improper integral:
e4t
cos(3t) e
dt =
lim
T00
if s + 4
or
4t
e" cos(3t) e-st dt =
lim sin(3T)/3
T00
if s = 4. help
(formulas)
b. For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of et cos(3t)?
s>4
help (inequalities)
c. Evaluate the existing limit to compute the Laplace transform of et cos(3t) on the domain you determined in the previous part:
F(s) = L {e# cos(3t)} =
help (formulas)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20ef5b89-bdf5-4ebf-bc1c-34f412b810c9%2F873b06ca-8bd4-42d2-96e5-dcc38374d0fd%2Fvq3jdib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:eat
cos(bt) dt =
a cos(bt) + b sin(bt)
+ C.
eat
a2 + 62
a. Use this antiderivative to compute the following improper integral:
e4t
cos(3t) e
dt =
lim
T00
if s + 4
or
4t
e" cos(3t) e-st dt =
lim sin(3T)/3
T00
if s = 4. help
(formulas)
b. For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of et cos(3t)?
s>4
help (inequalities)
c. Evaluate the existing limit to compute the Laplace transform of et cos(3t) on the domain you determined in the previous part:
F(s) = L {e# cos(3t)} =
help (formulas)
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