Defining Continuity at a Point Practice Test

Yes; the limit exists, so continuity holds even if $f(0)$ were different.

No; $f(0)$ is undefined since $\sin 0/0$ is undefined.

No; $\lim_{x\to0}\sin x/x$ does not exist because $\sin 0=0$.

No; $\lim_{x\to0}f(x)=0$ but $f(0)=1$.

Yes; $f(0)=1$ and $\lim_{x\to0}f(x)=1$, so $\lim_{x\to0}f(x)=f(0)$.