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Thread: Help with this calculus related question

  1. #1
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    Help with this calculus related question

    For f(x) = x + e^-x
    Find, if they exist, the equations of any asymptotes.
    How do I do this?Thanks!
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  2. #2
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    Re: Help with this calculus related question

    First check for vertical asymptotes. Are there any values $x=a$ such that $\displaystyle \lim_{x\to a} f(x)$ does not exist because it approaches positive or negative infinity?

    Next, check for horizontal asymptotes. These take the form:
    $y=\lim_{x\to \infty} f(x)$
    $y=\lim_{x\to -\infty} f(x)$

    Finally, you can try
    $\lim_{x\to \infty} (f(x)-mx-b) = 0$
    $\lim_{x\to -\infty} (f(x)-mx-b) = 0$
    If you find valid $m,b$ but you cannot find any value $a$ such that $f(a)=ma+b$ then $y=mx+b$ is an asymptote.

    Trying all of these, $y=x$ is the only asymptote.
    Thanks from winkyinky146
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