Wiskunde Multiple Choice Vraag

	Welke uitspraak is waar ?
A.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=+\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=+\infty\)
B.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=+\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=-\infty \)
C.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=-\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=+\infty\)
D.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=-\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=-\infty\)
E.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}\quad\text{bestaat niet}\)

Welke uitspraak is waar ?

\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=+\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=+\infty\)

\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=+\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=-\infty \)

\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=-\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=+\infty\)

\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=-\infty\;\;\text{en}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=-\infty\)

\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}\quad\text{bestaat niet}\)

	Which statement is correct ?
A.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=\infty\;\;\text{and}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=\infty \)
B.	\(\ \displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=\infty\;\;\text{and}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=-\infty\)
C.	\(\displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=-\infty\;\;\text{and}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=\infty \)
D.	\(\ \displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}=-\infty\;\;\text{and}\;\;\displaystyle\lim_{x\to 0}\,\frac{1}{1-\sin x-\cos x}=-\infty\)
E.	\(\ \displaystyle\lim_{x\to 0}\,\frac{x}{x-\sin x}\quad\text{does not exist}\)