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Mathematik-Online problems:

Problem 130: Derivations and 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
For which $ x$ the following functions are differentiable? Determine in each case the derivation of $ f$ .

a) $ {\displaystyle{f(x)=\sqrt{\frac{1+x}{1-x}}}}$ b) $ {\displaystyle{f(x)=x^{\,\sqrt{\tan x}}}}$ c) $ {\displaystyle{f(x)=x^2{\rm {e}}^{-x^2}\sinh x}}$
Test if the following limits exist and if so, calculate them.
d) $ {\displaystyle{\lim_{x\to 0+0}\, x^{-\sinh x}}}$ e) $ {\displaystyle{\lim_{x\to 0}\, \frac{{\rm {e}}^x-{\rm {e}}^{-x}-2x}{x-\sin x}}}$    


(Authors: /Höfert)

see also:

[Solutions]
  automatisch erstellt am 13. 12. 2007