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# Show that if $0 \le f(t) \le Me^{at}$ for $t \ge 0$, where $M$ and $a$ are constants, then the Laplace transform $F(s)$ exists for $s > a$.

## Hence $\int_{0}^{+\infty} M e^{(a-s) t} d t$ is convergent and then by the Comparison Theoremwe have that $\int_{0}^{+\infty} f(t) e^{-s t} d t$ is convergent and therefore the Laplace transform$F(s)$ exists.

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

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### Video Transcript

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WZ

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp