upper bound of exponential function I am looking for a tight upper bound of exponential function (or sum of exponential functions):
$e^x<f(x)\;$ when $ \;x<0$ 
or
$\displaystyle\sum_{i=1}^n e^{x_i} < g(x_1,...,x_n)\;$ when $\;x_i<0$ 
Thanks a lot!

How about $e^{-x}\leq c(\gamma)(\frac{1}{1+x})^\gamma$ for non-negative $x$?
