Question

Please help me solve the following problem. Show that the limit does not exist by considering the limits (x,y)-->(0,0) along the coordinate axes. Click to see the limit...

Answer 1

\[\lim_{(x,y) \rightarrow (0,0)}\frac{ 3 }{ x ^{2} +2y ^{2}}\]

Answer 2

When you go along the x-axis, you fix y=0, so it looks like this: \[\lim_{x\rightarrow0} \frac{3}{x^2}=\infty\]
Same analysis for y-axis, where x=0.

Answer 3

When x=0 the limit is also positive infinity so how does the limit not exist?

Answer 4

If both limits are the same doesn't that indicate that the limit does exist?

Answer 5

@blockcolder

Answer 6

nvm i got it...