Mathematik-Online problems: Problem 127: Types of Discontinuity

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	Mathematik-Online problems:
	Problem 127: Types of Discontinuity

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 $D\subset\mathbb{R}$ of each of the following functions, and test the behaviour of

for the critical points. What types of discontinuity appear?

a) $f(x) = \displaystyle \cos\sqrt{x} +\sqrt{\cos x}$ b) $f(x) = \sin\,\frac{1}{x}$

c) $f(x) = \displaystyle\left\{\begin{array}{rl} {\displaystyle{\frac{x^4+2x^2-3}{... ...\vert x\vert\neq 1 \\ -4\,\,, & {\mbox{if}} \ \vert x\vert=1\end{array}\right.$ d) $f(x) = \displaystyle\left\{\begin{array}{rl} 1, & {\mbox{if}} \ x\geq 0 \\ -1, & {\mbox{if}} \ x<0 \end{array}\right.$

(Authors: Apprich/Höfert)

see also:

Keyword: Continuity
Keyword: Derivative: complex function

[Solutions]

automatisch erstellt am 14. 10. 2004

a) $f(x) = \displaystyle \cos\sqrt{x} +\sqrt{\cos x}$	b) $f(x) = \sin\,\frac{1}{x}$
c) $f(x) = \displaystyle\left\{\begin{array}{rl} {\displaystyle{\frac{x^4+2x^2-3}{... ...\vert x\vert\neq 1 \\ -4\,\,, & {\mbox{if}} \ \vert x\vert=1\end{array}\right.$	d) $f(x) = \displaystyle\left\{\begin{array}{rl} 1, & {\mbox{if}} \ x\geq 0 \\ -1, & {\mbox{if}} \ x<0 \end{array}\right.$