Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to -\infty}\; \left ( \sqrt{x^2+5x}-\sqrt{x^2+x} \right )=$	A. 2
B. 3
C. − 2
D. 0
E. − 3

$\\\displaystyle\lim_{x\to-\infty}\;\left(\sqrt{x^2+5x}-\sqrt{x^2+x}\right)=\lim_{x\to-\infty}\;\frac{x^2+5x-(x^2+x)}{\sqrt{x^2+5x}+\sqrt{x^2+x}}\\=\lim_{x\to-\infty}\;\frac{5x-x}{\sqrt{x^2+5x}+\sqrt{x^2+x}}=\lim_{x\to-\infty}\;\frac{4x}{-x\sqrt{1+\frac5x}-x\sqrt{1+\frac1x}}\\=\lim_{x\to-\infty}\;\frac{-4}{\sqrt{1+\frac5x}+\sqrt{1+\frac1x}}=\frac{-4}{1+1}=-2$

^{gricha - v2341 - 2.4.10}