Mathematik-Online problems: Problem 103: Limits of Functions

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	Mathematik-Online problems:
	Problem 103: Limits of Functions

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Test if the limits exist and calculate them, if so.

a) ${\displaystyle{\lim_{x\rightarrow 2}\left(\frac{1}{2-x}-\frac{12}{8-x^3}\right)}}$ b) ${\displaystyle{\lim_{x\rightarrow -3}\,\, \frac{x^2-9}{2x^3+54}}}$ c) ${\displaystyle{\lim_{x\rightarrow 0} \, \left(\frac{1}{2}\right)^{\!\!-1/x^2}}}$

d) ${\displaystyle{\lim_{x\rightarrow \frac{\pi}{2}} \, \frac{\sin 2x}{\tan x}}}$ e) ${\displaystyle{\lim_{x\rightarrow\infty}\, \frac{\sqrt{x+1}-\sqrt{3x+2}}{\sqrt{x}}}}$

Solution:

Lösung (german)

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automatisch erstellt am 19. 1. 2017

a)	${\displaystyle{\lim_{x\rightarrow 2}\left(\frac{1}{2-x}-\frac{12}{8-x^3}\right)}}$	b)	${\displaystyle{\lim_{x\rightarrow -3}\,\, \frac{x^2-9}{2x^3+54}}}$	c)	${\displaystyle{\lim_{x\rightarrow 0} \, \left(\frac{1}{2}\right)^{\!\!-1/x^2}}}$
d)	${\displaystyle{\lim_{x\rightarrow \frac{\pi}{2}} \, \frac{\sin 2x}{\tan x}}}$	e)	${\displaystyle{\lim_{x\rightarrow\infty}\, \frac{\sqrt{x+1}-\sqrt{3x+2}}{\sqrt{x}}}}$