Difference between revisions of "Asymptote (geometry)"
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The vertical asymptote can be found by finding values of <math>x</math> that make the function undefined. One of the common ways is to have the function divided by zero, which is undefined. This can be shown by example. | The vertical asymptote can be found by finding values of <math>x</math> that make the function undefined. One of the common ways is to have the function divided by zero, which is undefined. This can be shown by example. | ||
− | + | ===Example Problem=== | |
− | |||
Find the vertical asymptotes of <math>\frac{1}{x^{2}}</math>. | Find the vertical asymptotes of <math>\frac{1}{x^{2}}</math>. | ||
− | To find the vertical asymptotes, <math>x^2</math> must equal | + | To find the vertical asymptotes, <math>x^2</math> must equal zero. Solving the equation: |
− | <math>\begin{eqnarray*}x^2&=& | + | <math>\begin{eqnarray*}x^2&=&0\\x&=&\boxed{0\end{eqnarray*}</math> |
− | So the vertical asymptote is <math>x= | + | So the vertical asymptote is <math>x=0</math>, or just the y-axis |
== Slanted Asymptotes == | == Slanted Asymptotes == | ||
{{stub}} | {{stub}} |
Revision as of 22:06, 8 November 2007
This is an AoPSWiki Word of the Week for Nov 8-14 |
- For the vector graphics language, see Asymptote (Vector Graphics Language).
An asymptote is a line or curve that a certain function approaches.
Asymptotes can be of three different kinds: horizontal, vertical or slanted (oblique).
Horizontal Asymptotes
Vertical Asymptotes
The vertical asymptote can be found by finding values of that make the function undefined. One of the common ways is to have the function divided by zero, which is undefined. This can be shown by example.
Example Problem
Find the vertical asymptotes of .
To find the vertical asymptotes, must equal zero. Solving the equation:
$\begin{eqnarray*}x^2&=&0\\x&=&\boxed{0\end{eqnarray*}$ (Error compiling LaTeX. ! Missing \endgroup inserted.)
So the vertical asymptote is , or just the y-axis
Slanted Asymptotes
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