Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De limiet $\displaystyle \: \lim_{x \to +\infty }\frac{x^x}{(x+1)^x}$ is gelijk aan	A. 0
B. e
C.
D. 1
E.

$\displaystyle \: \lim_{x \to \infty }\frac{x^x}{(x+1)^x}=$	A. 0
	B. e
	C.
	D. 1
	E. ∞

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to +\infty}\frac{x^x}{(x+1)^x}=\displaystyle \lim_{x \to +\infty}\left (\frac{x}{x+1} \right )^x=\displaystyle \lim_{x \to +\infty}\left (\frac{x+1}{x} \right )^{-x}\\=\displaystyle \lim_{x \to +\infty}\left (1+\frac{1}{x} \right )^{-x}=\frac{1}{\displaystyle \lim_{x \to +\infty}\left (1+\frac{1}{x} \right )^x }= \frac 1e$