Determine which of the following statements are true and which are false. Enter the T or F in front of each statement.
Remember that $x\in(-1,1)$ is the same as $-1 < x < 1$
and $x\in[-1,1]$ means $-1 \le x \le 1$.

1. The function $f(x)=x^2$ with domain $x\in(-3,3)$ has at least one input which produces a smallest output value.
2. The function $\sin(x)$ on the domain $x\in(-\pi/2,\pi/2)$ has at least one input which produces a smallest output value.
3. The function $f(x)=x^2$ with domain $x\in[-3,3]$ has at least one input which produces a largest output value.
4. The function $\sin(x)$ on the domain $x\in[-\pi/2,\pi/2]$ has at least one input which produces a largest output value.
5. The function $\sin(x)$ on the domain $x\in[-\pi/2,\pi/2]$ has at least one input which produces a smallest output value.