I got DNE for all four of these (zero in the denominator). I am a little skeptical about submitting 4 answers as DNE, so I need your help.

I will show you what I have gotten done on these four. Can you let me know if they really are DNE, or if you were able to get further on certain problems (without telling me the answer).

[Problem 1]

$\displaystyle \\\begin{array}{c}\lim\\x\rightarrow-3\end{array} \ \ \frac{6}{x+3}$

Can't factor this one and don't see a reason to multiply by the conjugate, so I plugged in for X and got DNE.

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[Problem 2]

$\displaystyle \\\begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{x-9}{x^{2}-14x+45} \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{x-9}{(x-9)(x-5)} \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{1}{(x-5)} \\ \\ \\ \frac{1}{5-5} \\ \\ \\ \frac{1}{0}$

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[Problem 3]

$\displaystyle \\\begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{5x^{2}-125}{x^{2}-10x+25} \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{5(x^{2}-25)}{(x-5)(x-5)} \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{5(x-5)(x+5)}{(x-5)(x-5)} \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow5\end{array} \ \ \frac{5(x+5)}{(x-5)} \\ \\ \\ \frac{50}{0}$

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[Problem 4]

$\displaystyle \\\begin{array}{c}\lim\\x\rightarrow4\end{array} \ \ \frac{x-2}{\sqrt{x}-2} \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow4\end{array} \ \ \left(\frac{x-2}{\sqrt{x}-2}\right) \left(\frac{\sqrt{x}+2}{\sqrt{x}+2}\right) \\ \\ \\ \begin{array}{c}\lim\\x\rightarrow4\end{array} \ \ \frac{(x-2)(\sqrt{x}+2)}{x-4} \\ \\ \\ \frac{8}{0}$