1. LIMIT/Absolute Maximum

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

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

2. Originally Posted by Shyam
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.