M.C. Question

Alle waarden α ∈ [ 0, ] waarvoor geldt dat $\large \lim_{x\rightarrow +\infty }\left ( tan\, \alpha \right )^x=+\infty$ worden gegeven door het interval	A. ] 1, ]
	B. [ 0, ]
	C. [ , [
	D. ] , ]
	E. ] , [

[ 6-4151 - op net sinds 18.7.12-(E)-3.11.2023 ]

Translation in E N G L I S H

All of the values α ∈ [ 0, ] for which $\lim_{x\rightarrow \infty }\left ( tan\, \alpha \right )^x=\infty$ are given by the interval	A. ( 1, ]
	B. [ 0, ]
	C. [ , )
	D. ( , ]
	E. ( , )

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\\text{We steunen op het feit dat}\\\displaystyle \lim_{x \to +\infty}a^x= +\infty\quad als\;a>1\\\displaystyle \lim_{x \to +\infty}a^x= 0 \qquad \;als\;0<a<1\\\displaystyle \lim_{x \to +\infty}a^x= 1 \qquad \;als\;a=1\\ \tan\alpha >1\;als\; \alpha \in \Bigr] \frac{\pi}{4},\frac{\pi}{2}\Bigl[\\(\tan \frac{\pi}{4}=1,\;\tan \frac{\pi}{2}\;bestaat\;niet)$