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The Laplace transform F(s) of the exponential function, f(t)=e^(at) when t≥0, where a is a constant and (s−a)>0, is

1. 1/(s+a)
2. 1/(s−a)
3. 1/(a−s)
4. ∞

Correct answer: 1/(s−a)

Solution

The Laplace transform of the function f(t)=e^(at) is derived by integrating e^(at) multiplied by e^(-st) over the interval from 0 to infinity, resulting in the expression 1/(s-a) when the condition (s-a)>0 is satisfied.

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