== The Laplace Transform turns a given function f = f(t) into a new function F = F(8) by way of an improper integral: F(s) = √ e™" f(t) dt. est Suppose f(t)=8t - 10. 8 (a) Find the set of real numbers & for which the improper integral defining F(s) converges. Answer in interval notation. (To enter co, type "inf"; for-oo, type "-inf".) Answer: (2s+8)/s^2 (b) Find a simple formula for F(s), valid on the interval described in part (a). Answer: F(s) (2s+8)/s^2 =
== The Laplace Transform turns a given function f = f(t) into a new function F = F(8) by way of an improper integral: F(s) = √ e™" f(t) dt. est Suppose f(t)=8t - 10. 8 (a) Find the set of real numbers & for which the improper integral defining F(s) converges. Answer in interval notation. (To enter co, type "inf"; for-oo, type "-inf".) Answer: (2s+8)/s^2 (b) Find a simple formula for F(s), valid on the interval described in part (a). Answer: F(s) (2s+8)/s^2 =
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Transcribed Image Text:==
The Laplace Transform turns a given function f = f(t) into a new function F = F(8) by way of an
improper integral:
F(s) = √ e™" f(t) dt.
est
Suppose f(t)=8t - 10.
8
(a) Find the set of real numbers & for which the improper integral defining F(s) converges. Answer in
interval notation. (To enter co, type "inf"; for-oo, type "-inf".)
Answer:
(2s+8)/s^2
(b) Find a simple formula for F(s), valid on the interval described in part (a).
Answer: F(s) (2s+8)/s^2
=
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