Multiple choice

In what range should Re(s) remain so that the Laplace transform of the function $e^{(x + 2)t+5}$ exists?

  1. Re(s) > a + 2

  2. Re(s) > a + 7

  3. Re(s) < 2

  4. Re(s) > a + 5
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A Correct answer
Explanation

$\text{We have} \hspace{0.2cm} f(t) = e^{(a+2)t+5} = e^5 . e^{(a+2)t} \\ \text{Taking laplace transform we get} \\ F(s) = e^5 \begin{bmatrix} \ \frac{1}{s - (a+2)} \end{bmatrix} \hspace{2cm} \text{Thus} \hspace{0.2cm}Re(s) > (a+2)$

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