Question

lim(x,y)-(0,0) sinx/y exists.

Answer 1

Solution:

$\lim _{(x,y)\rightarrow(0,0)} \sin (\frac xy)$

Let's calculate this in two different ways.

Along $x=0$

$\lim _{(x,y)\rightarrow(0,y)} \sin (\frac 0y)=0$

Now, along $y=0$

$\lim _{(x,y)\rightarrow(x,0)} \sin (\frac x0)=\infty$

Since, both the limits are unequal, limit of given function does not exist.