Mathematik-Online problems: Problem 130: Derivations and Limits of Functions

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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

the following functions are differentiable? Determine in each case the derivation of

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)

Solution:

automatisch erstellt am 13. 12. 2007