Difference between revisions of "Math 22 Asymptotes"

Revision as of 06:52, 4 August 2020

 If  $f(x)$  approaches infinity (or negative infinity) as  $x$  approaches  $c$  from the right or from the left, then the line

Example: Find the limit below:

1) $\lim _{x\to 3^{-}}{\frac {-2}{x-3}}$

Solution:
Important: $\lim {\frac {\text{constant}}{0}}$ is either $\infty$ or $-\infty$
Notice $x\to 3^{-}$ , so $x<3$ , then $x-3<0$ , hence the denominator will be "negative".
Therefore, $\lim _{x\to 3^{-}}{\frac {-2}{x-3}}={\frac {\text{negative}}{\text{negative}}}=\infty$

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@@ Line 2: / Line 2: @@
    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: &nbsp;
+|-
+|'''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>
+|}
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