Use Theorem 7. 1. 1 to find $\mathscr{L}\{f(t)\}$. $f(t)=2 t^{4}$

Use Definition 7. 1. 1 to find $\mathscr{L}\{f(t)\}$.

$$f(t)=\left\{\begin{array}{lr} \sin t, & 0 \leq t<\pi \\ 0, & t \geq \pi \end{array}\right.$$

Use Definition 7.1 to find $\mathscr{L}\{f(t)\}.$

$$f(t)=\left\{\begin{array}{lr}{4,} & {0 \leq t<2} \\ {0,} & {t \geq 2}\end{array}\right.$$

Use Definition 7. 1. 1 to find $\mathscr{L}\{f(t)\}$.

$$f(t)=\left\{\begin{array}{rr} -1, & 0 \leq t<1 \\ 1, & t \geq 1 \end{array}\right.$$

Let

$$x\ \mapsto\ [[x]]$$

denote the greatest integer function. Determine the points of continuity of the function

$$f(x) := x - [[x]], x \in \mathbb{R}.$$

Determine whether the following functions are continuous at a. Use the continuity checklist to justify your answer. f(x)=$\sqrt { x - 2 }$; a=1