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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 $ f$ 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:


[Solutions]

  automatisch erstellt am 14. 10. 2004