# Math Help - Limits of 2 Variables

1. ## Limits of 2 Variables

lim ( cos(x)-1 + (x^2)/2 ) / (x^4 + y^4)
(x,y) - (0,0)

To evaluate this limit do i use L'Hospital's rule a few times to get it down to a solution or am i reading into it too much and is easier way?

Cheers

2. Originally Posted by monster
lim ( cos(x)-1 + (x^2)/2 ) / (x^4 + y^4)
(x,y) - (0,0)

To evaluate this limit do i use L'Hospital's rule a few times to get it down to a solution or am i reading into it too much and is easier way?

Cheers
First approach (0,0) from different directions. Along the y axis (x=0) then

$\lim_{y \to 0} \frac{0}{y^4} = 0$.

Then along the x axis (y=0) then

$\lim_{x \to 0} \frac{ \cos x - 1 + \frac{1}{2}x^2}{x^4}$ (use L'Hopital's rule on this one)