$\displaystyle lim_{x\to_\infty} (1+3x-3x^3+5x^5) $
Is there limit ?
if yes , show the limit
if not prove ...
In that case, put $\displaystyle e^{ln}$ in front of the expression to bring down the exponent - then put the $\displaystyle x^2$ (which was part of the exponent) in the denominator while the really long term with all the x's is in the numerator and use L'Hopital's rule. Give it a shot.