Solved: Theorem 6 in Section 7.3 can be expressed in terms

Chapter 7, Problem 33E

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QUESTION:

Theorem 6 in Section 7.3 can be expressed in terms of the inverse Laplace transform as

\(\mathscr{\mathcal { L }}^{1}\left\{\frac{d^{n} F}{d s^{n}}\right\}(t)=(-t)^{n} f(t)\)

where \(\mathscr{\mathscr { L }}^{-1}\{F)\). Use this equation in Problems 33–36 to compute \(\mathscr{L}^{-1}\{F\}\).

\(F(s)=\ln \left(\frac{s+2}{s-5}\right)\)

Equation transcription:

Text transcription:

{ { L }}^{1}{frac{d^{n} F}{d s^{n}}}(t)=(-t)^{n} f(t)

f=r{L}^{-1}{F}

{{ L }}^{-1}\{F)

{L}^{-1}{F\}

F(s)=ln (\frac{s+2}{s-5})

Questions & Answers

QUESTION:

Theorem 6 in Section 7.3 can be expressed in terms of the inverse Laplace transform as

\(\mathscr{\mathcal { L }}^{1}\left\{\frac{d^{n} F}{d s^{n}}\right\}(t)=(-t)^{n} f(t)\)

where \(\mathscr{\mathscr { L }}^{-1}\{F)\). Use this equation in Problems 33–36 to compute \(\mathscr{L}^{-1}\{F\}\).

\(F(s)=\ln \left(\frac{s+2}{s-5}\right)\)

Equation transcription:

Text transcription:

{ { L }}^{1}{frac{d^{n} F}{d s^{n}}}(t)=(-t)^{n} f(t)

f=r{L}^{-1}{F}

{{ L }}^{-1}\{F)

{L}^{-1}{F\}

F(s)=ln (\frac{s+2}{s-5})

ANSWER:

Solution:

Step 1:

In this problem we need to determine .

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