Question

Hi, limit problem in 3d.
lim as (x,y)approaches(0,1) ysin(x)/x(y+1)

Answer 1

I know that I can say that the lim of x as it approaches 0 times the serperate limit for y approaching 1 can be mult together to find limit for xy.

Answer 2

So lim x approaches 0 oj sin(x)/x multiplied by the limit of y as it approaches 1 of y/(y+1)

Answer 3

But would the limit of x as it approaches 0 be undefined?

Answer 4

Hmm I think you've got the right idea here.
You just need to remember an important identity from calc 1,\[\Large\bf\sf \lim_{x\to 0}\frac{\sin x}{x}\quad=\quad 1\]For small x, sinx acts like x.

So as you get closer and closer to zero, the relationship is behaving like x/x.

Answer 5

And even though it cant actually equal zero...when it gets close it just behaves like x/x? Thanks (;