Solution Found!
Initial Value Theorem. Apply the relation to argue that
Chapter 7, Problem 37E(choose chapter or problem)
Initial Value Theorem. Apply the relation
\(\mathscr{L}\left(f^{\prime}\right\}(s)=\int_{0}^{\infty} e^{-s t} f^{\prime}(t) d t=s \mathscr{L}\{f(s)-f(0)\)
to argue that for any function whose derivative is piecewise continuous and of exponential order on \([0, \infty]\),
\(f(0)=\lim _{S \rightarrow \infty} S \mathscr{L}\{f(s)\).
Equation transcription:
Text transcription:
{L}(f^{prime}}(s)=int{0}^{infty} e^{-s t} f^{prime}(t) d t=s{L}\{f(s)-f(0)
[0, infty]
f(0)=lim {S rightarrow infty} S{L}\{f(s)
Questions & Answers
QUESTION:
Initial Value Theorem. Apply the relation
\(\mathscr{L}\left(f^{\prime}\right\}(s)=\int_{0}^{\infty} e^{-s t} f^{\prime}(t) d t=s \mathscr{L}\{f(s)-f(0)\)
to argue that for any function whose derivative is piecewise continuous and of exponential order on \([0, \infty]\),
\(f(0)=\lim _{S \rightarrow \infty} S \mathscr{L}\{f(s)\).
Equation transcription:
Text transcription:
{L}(f^{prime}}(s)=int{0}^{infty} e^{-s t} f^{prime}(t) d t=s{L}\{f(s)-f(0)
[0, infty]
f(0)=lim {S rightarrow infty} S{L}\{f(s)
ANSWER:Solution
Step 1 of 5
In this problem we have to prove the given condition.