Multiple Choice 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. $]\,1,\frac{\pi}2]$
	B. $[\,0,\frac{\pi}2]$
	C. $[\frac{\pi}4,\frac{\pi}2[$
	D. $]\frac{\pi}4,\frac{\pi}2]$
	E. $]\frac{\pi}4,\frac{\pi}2[$

[ 6-4151 - op net sinds 18.7.12-(E)-13.6.2025 ]

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. $(\,1,\frac{\pi}2]$
	B. $[\,0,\frac{\pi}2]$
	C. $[\frac{\pi}4,\frac{\pi}2)$
	D. $(\frac{\pi}4,\frac{\pi}2]$
	E. $(\frac{\pi}4,\frac{\pi}2)$

Oplossing - Solution

$\begin{aligned} &\text{We steunen op het feit dat}\\&\displaystyle \lim_{x \to +\infty}a^x= +\infty\quad als\;a>1\\&\displaystyle \lim_{x \to +\infty}a^x= 0 \qquad \;als\;0<a<1\\&\displaystyle \lim_{x \to +\infty}a^x= 1 \qquad \;als\;a=1\\ &\tan\alpha >1\;als\; \alpha \in \Bigr] \frac{\pi}{4},\frac{\pi}{2}\Bigl[\\&(\tan \frac{\pi}{4}=1,\;\tan \frac{\pi}{2}\;bestaat\;niet) \end{aligned}$

Alle waarden α ∈ [ 0, ] waarvoor geldt dat $\large \lim_{x\rightarrow +\infty }\left ( tan\, \alpha \right )^x=+\infty$ worden gegeven door het interval	A. \(]\,1,\frac{\pi}2]\)
	B. \([\,0,\frac{\pi}2]\)
	C. \([\frac{\pi}4,\frac{\pi}2[\)
	D. \(]\frac{\pi}4,\frac{\pi}2]\)
	E. \(]\frac{\pi}4,\frac{\pi}2[\)

All of the values α ∈ [ 0, ] for which $\lim_{x\rightarrow \infty }\left ( tan\, \alpha \right )^x=\infty$ are given by the interval	A. \((\,1,\frac{\pi}2]\)
	B. \([\,0,\frac{\pi}2]\)
	C. \([\frac{\pi}4,\frac{\pi}2)\)
	D. \((\frac{\pi}4,\frac{\pi}2]\)
	E. \((\frac{\pi}4,\frac{\pi}2)\)