How to find the vertical assimptote

  • Thread starter transgalactic
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In summary, a vertical asymptote is a vertical line on a graph that represents a value where the function approaches infinity or negative infinity. To find the vertical asymptote of a function, set the denominator of the function equal to zero and solve for the variable. A function can have multiple vertical asymptotes if there are multiple values that make the denominator equal to zero. The vertical asymptote represents values on the graph where the function is undefined or approaches infinity. To verify the vertical asymptote on a graph, look for a vertical line that the graph approaches but does not cross, or plug in values close to the vertical asymptote and see if the function approaches infinity or negative infinity.
  • #1
transgalactic
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[tex]
f(x)=\frac{1}{1+ln|x|}\\
[/tex]
[tex]
x\neq \frac{1}{e}\\
[/tex]
[tex]
x\neq \frac{-1}{e}\\
[/tex]
[tex]
lim_{x->\frac{1}{e}^+}\frac{1}{1+ln|x|}=\\
[/tex]
[tex]
lim_{x->\frac{1}{e}^-}\frac{1}{1+ln|x|}=\\
[/tex]
i can't immagine ithe values in this function
??
 
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  • #2
First, 1/e is a postive number so you can just drop the absolute value.

Second, ln e-1= -1. Since ln(x) is an increasing function, if x< e-1, ln(x)< -1 and if x> e-1, ln(x)> -1. That's all you need.
 

1. What is a vertical asymptote?

A vertical asymptote is a vertical line on a graph that represents a value where the function approaches infinity or negative infinity.

2. How do I determine the vertical asymptote of a function?

To find the vertical asymptote of a function, set the denominator of the function equal to zero and solve for the variable. The resulting value will be the vertical asymptote.

3. Can a function have more than one vertical asymptote?

Yes, a function can have multiple vertical asymptotes. This can occur when there are multiple values that make the denominator of the function equal to zero.

4. What does the vertical asymptote represent?

The vertical asymptote represents values on the graph where the function is undefined or approaches infinity. It can also help determine the behavior of the function as it approaches these values.

5. How can I verify the vertical asymptote on a graph?

To verify the vertical asymptote on a graph, look for a vertical line that the graph approaches but does not cross. You can also plug in values close to the vertical asymptote and see if the function approaches infinity or negative infinity.

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