Mathematik-Online problems: Problem 102: Continuity of Functions

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	Mathematik-Online problems:
	Problem 102: Continuity 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

Find the domain and codomain of the given functions $f: \mathbb{R}\longrightarrow\mathbb{R}$ , and test for which

is continuous respectively one-side continuous.

a) ${\displaystyle{f(x)=x^4-2+\sqrt{2-\frac{1}{x^4}}}}$ b) ${\displaystyle{f(x)=\frac{x^3+2x^2-11x-12}{x^4-10x^3+22x^2-10x+21}}}$

c) $f(x)=\sqrt{{\rm {ln}}\,x}+{\rm {ln}}\,\sqrt{x}$ d) $f(x)=\tan x\cdot \sin \frac{1}{x}$

e) $f(x)=\max\,\{z\in\mathbb{Z} \mid z\leq x\}$

(Authors: Apprich/Höfert)

Solution:

Lösung (german)

[Links]

automatisch erstellt am 14. 10. 2004

a)	${\displaystyle{f(x)=x^4-2+\sqrt{2-\frac{1}{x^4}}}}$	b)	${\displaystyle{f(x)=\frac{x^3+2x^2-11x-12}{x^4-10x^3+22x^2-10x+21}}}$
c)	$f(x)=\sqrt{{\rm {ln}}\,x}+{\rm {ln}}\,\sqrt{x}$	d)	$f(x)=\tan x\cdot \sin \frac{1}{x}$
e)	$f(x)=\max\,\{z\in\mathbb{Z} \mid z\leq x\}$