Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. A statement is true only if it is true for all possibilities. You must get all of the answers correct to receive credit.

1. If $\displaystyle \lim_{x\rightarrow 7} [f(x)g(x)]$ exists, then the limit is $f(7)g(7)$
2. If $\displaystyle \lim_{x\rightarrow 6} f(x) = 5$ and $\displaystyle \lim_{x\rightarrow 6} g(x) = 0$, then $\displaystyle \lim_{x\rightarrow 6} [f(x)/g(x)]$ does not exist
3. If $f'(7)$ exists, then then the limit $\displaystyle \lim_{x\rightarrow 7} f(x)$ is $f(7)$
4. If $\displaystyle \lim_{x\rightarrow 6} f(x) = 0$ and $\displaystyle \lim_{x\rightarrow 6} g(x) = 5$, then $\displaystyle \lim_{x\rightarrow 6} [f(x)/g(x)]$ does not exist
5. If $\displaystyle \lim_{x\rightarrow 6} f(x) = \infty$ and $\displaystyle \lim_{x\rightarrow 6} g(x) = \infty$, then $\displaystyle \lim_{x\rightarrow 6} [f(x)-g(x)] =0$