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Mathematik-Online problems:

Problem 112: Curve Sketching, Arc Tangent

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
Given the function

$\displaystyle f(x)=\arctan\left(\frac{2x}{1-x^2}\right). $


a)
For which $ x\in\mathbb{R}$ $ f$ is defined?
b)
Test $ f$ for symmetry, roots, lokal extremums and inflection points.
c)
Find the right- and left-hand limit of $ f$ and $ f'$ at $ x=1$ and $ x=-1$. What's the behaviour of$ f$ for $ \vert x\vert\longrightarrow\infty$?
d)
Sketch the graph of the function $ f$.

(Authors: /Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004