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Thread: LIMIT/Absolute Maximum

  1. #1
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    LIMIT/Absolute Maximum

    Let $\displaystyle g(x) = xe^{-x}+be^{-x}$, where b is a constant.
    Find

    $\displaystyle \mathop {\lim }\limits_{x \to \infty } g\left( x \right)$
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by Shyam View Post
    Let $\displaystyle g(x) = xe^{-x}+be^{-x}$, where b is a constant.
    Find

    $\displaystyle \mathop {\lim }\limits_{x \to \infty } g\left( x \right)$

    $\displaystyle e^{x}$ grows faster than x, so $\displaystyle \frac{x}{e^x}$ goes zero. The other term $\displaystyle \frac{b}{e^x}$ clearly goes to zero as well. So the overall limit is zero.
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