Graph f(x)=1/(1+e^(1/x))

Math
Find where the expression is undefined.
The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes
Evaluate to find the horizontal asymptote.
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Take the limit of each term.
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Split the limit using the Limits Quotient Rule on the limit as approaches .
Evaluate the limit of which is constant as approaches .
Split the limit using the Sum of Limits Rule on the limit as approaches .
Evaluate the limit of which is constant as approaches .
Move the limit into the exponent.
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Simplify the denominator.
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Anything raised to is .
Add and .
List the horizontal asymptotes:
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
No Vertical Asymptotes
Horizontal Asymptotes:
No Oblique Asymptotes
Graph f(x)=1/(1+e^(1/x))

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