# limit problem

• Jan 30th 2010, 10:31 AM
gilyos
limit problem
$\displaystyle lim_{x\to_\infty} (1+3x-3x^3+5x^5)$

Is there limit ?

if yes , show the limit
if not prove ...
• Jan 30th 2010, 11:47 AM
running-gag
Quote:

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

Is there limit ?

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

Hi

The method consists in factoring out the maximum exponent

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

The parenthesis has limit 5 at infinite therefore you can conclude
• Jan 30th 2010, 12:28 PM
gilyos
This is the right problem

$\displaystyle lim_{x\to_\infty} (1+3x-3x^3+5x^5)^\frac{1}{x^2}$
• Jan 30th 2010, 12:31 PM
Lord Darkin
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. :)