Laplace transforms

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   The function $f(t) = e^{-3t}$ has Laplace transform $F(s) = \dfrac{1}{s + 3}$, valid for $s > -3$. Evaluate $F(s)$ at $s = 5$.

2. Warm-up

   The function $f(t) = e^{-t}$ has Laplace transform $F(s) = \dfrac{1}{s + 1}$, valid for $s > -1$. Evaluate $F(s)$ at $s = 10$.

3. Warm-up

   The function $f(t) = e^{4t}$ has Laplace transform $F(s) = \dfrac{1}{s - 4}$, valid for $s > 4$. Evaluate $F(s)$ at $s = 5$.

Problems shown under their original terms: Generated (template, solver-computed).