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Oblique Asymptotes


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 overview

Example:

$\displaystyle f(x)$ $\displaystyle =\frac{3x^3+7}{2x^2+5x}$    
$\displaystyle f'(x)$ $\displaystyle =\frac{6x^4+30x^3-28x-35}{(2x^2+5x)^2}$    

$\displaystyle \lim_{x \to \infty}f'(x)=\lim_{x \to -\infty}f'(x)=\frac{3}{2}
$

$\displaystyle \lim_{x \to \infty}\Big(f(x)-\Big(\frac{3}{2}x+a\Big)\Big)$ $\displaystyle =0$    
$\displaystyle \lim_{x \to \infty}\Big(\frac{-\frac{15}{2}x^2+7}{2x^2+5}-a\Big)$ $\displaystyle =0$    
$\displaystyle -\frac{15}{4}-a$ $\displaystyle =0$    
$\displaystyle a$ $\displaystyle =-\frac{15}{4}$    

Thus there exists oblique asymptotes on the left and on the right side: $ y=\frac{3}{2}x-\frac{15}{4}$

\includegraphics{schiefe}

(Authors: Jahn/Knödler)

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  automatisch erstellt am 8.  7. 2004