Mathematik-Online lexicon: Oblique Asymptotes

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	Mathematik-Online lexicon:
	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

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)

see also:

automatisch erstellt am 8. 7. 2004