# Thread: multivariable limit with 3 vars!

1. ## multivariable limit with 3 vars!

ok i got alright at the limits with two variables (to an extent haha)

but now i have this limit:

lim (x,y,z) --> (0,0,0) of (2(x^2)ycos(z))/(x^2 + y^2)

where do i start?

2. The variable z is only in the term $\cos z$ that is equal to 1 for z=0, so that the 'real' limit is...

$\displaystyle \lim_{(x,y) \rightarrow (0,0)} \frac{2\ x^{2}\ y}{x^{2} + y^{2}}$

Kind regards

$\chi$ $\sigma$

3. Originally Posted by BrianMath
ok i got alright at the limits with two variables (to an extent haha)

but now i have this limit:

lim (x,y,z) --> (0,0,0) of (2(x^2)ycos(z))/(x^2 + y^2)

where do i start?
Never mind.

4. $\left| \dfrac{2x^2ycos(z)}{x^2+y^2} \right| \leq 2y$

Use sandwich.