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Math Help - LIMIT/Absolute Maximum

  1. #1
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    LIMIT/Absolute Maximum

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

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

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

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