Difference between revisions of "Math 22 Asymptotes"
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If <math>f(x)</math> approaches infinity (or negative infinity) as <math>x</math> approaches <math>c</math> from the right or from the left, then the line | If <math>f(x)</math> approaches infinity (or negative infinity) as <math>x</math> approaches <math>c</math> from the right or from the left, then the line | ||
| + | '''Example''': Find the limit below: | ||
| + | |||
| + | '''1)''' <math>\lim_{x\to 3^-}\frac{-2}{x-3}</math> | ||
| + | {| class = "mw-collapsible mw-collapsed" style = "text-align:left;" | ||
| + | !Solution: | ||
| + | |- | ||
| + | |'''Important''': <math>\lim \frac{\text{constant}}{0}</math> is either <math>\infty</math> or <math>-\infty</math> | ||
| + | |- | ||
| + | |Notice <math>x\to 3^-</math>, so <math> x<3 </math>, then <math> x-3<0</math>, hence the denominator will be "negative". | ||
| + | |- | ||
| + | |Therefore, <math>\lim_{x\to 3^-}\frac{-2}{x-3}=\frac{\text{negative}}{\text{negative}}=\infty</math> | ||
| + | |} | ||
This page is under construction | This page is under construction | ||
Revision as of 06:52, 4 August 2020
Vertical Asymptotes and Infinite Limits
If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)}
approaches infinity (or negative infinity) as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
approaches Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c}
from the right or from the left, then the line
Example: Find the limit below:
1) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 3^-}\frac{-2}{x-3}}
| Solution: |
|---|
| Important: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim \frac{\text{constant}}{0}} is either Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \infty} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\infty} |
| Notice Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x\to 3^-} , so Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x<3 } , then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x-3<0} , hence the denominator will be "negative". |
| Therefore, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 3^-}\frac{-2}{x-3}=\frac{\text{negative}}{\text{negative}}=\infty} |
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This page were made by Tri Phan