Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{\underset{<}{x \to 5}}\: \frac{\sqrt{25-x^2}}{5-x}$ is gelijk aan	A. 1
B.
C.
D.
E. 5

$\displaystyle \lim_{x \to 5^-}\: \frac{\sqrt{25-x^2}}{5-x}$ is equal to	A. 1
B.
C.
D. ∞
E. 5

$\begin{aligned} \displaystyle\lim_{\scriptsize\begin{matrix}x\to5\\<\end{matrix}}\frac{\sqrt{25-x^2}}{5-x}=\displaystyle\lim_{\scriptsize\begin{matrix}x\to5\\<\end{matrix}}\frac{(\sqrt{25-x^2})(\sqrt{25+x^2})}{(5-x)(\sqrt{25+x^2})}=\displaystyle\lim_{\scriptsize\begin{matrix}x\to5\\<\end{matrix}}\frac{25-x^2}{(5-x^2)(\sqrt{25+x^2})}\\=\displaystyle\lim_{\scriptsize\begin{matrix}x\to5\\<\end{matrix}}\frac{(5-x)(5+x)}{(5-x)(\sqrt{25+x^2})}=\displaystyle\lim_{\scriptsize\begin{matrix}x\to5\\<\end{matrix}}\frac{5+x}{(\sqrt{25+x^2})}=\frac{10}{+0}=+\infty \end{aligned}$