# Math Help - limit problem

1. ## limit problem

$lim_{x\to_\infty} (1+3x-3x^3+5x^5)$

Is there limit ?

if yes , show the limit
if not prove ...

2. Originally Posted by gilyos
$lim_{x\to_\infty} (1+3x-3x^3+5x^5)$

Is there limit ?

if yes , show the limit
if not prove ...
Hi

The method consists in factoring out the maximum exponent

$1+3x-3x^3+5x^5 = x^5 \:\left(\frac{1}{x^5}+\frac{3}{x^4}-\frac{3}{x^2}+5 \right)$

The parenthesis has limit 5 at infinite therefore you can conclude

3. This is the right problem

$lim_{x\to_\infty} (1+3x-3x^3+5x^5)^\frac{1}{x^2}$

4. In that case, put $e^{ln}$ in front of the expression to bring down the exponent - then put the $x^2$ (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.