- #1
bayan
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Homework Statement
Find the limit (if it exists) and domain of the following function. (I do not need to use epsilon delta proof, just results on different curves to prove this)
[itex] \stackrel{lim}{_{(x,y)→(−1,0)}}[/itex] [itex] \frac {x(x+1)y^2}{(x+1)^2+y^2}[/itex]
Homework Equations
The Attempt at a Solution
Just by looking at function I can see that Domain is [itex]ℝ | x≠0, x≠-1, y≠0 , y^2≠-(x+1)^2|[/itex]Having graphed that function in Google I can see that at [itex](-1,0)[/itex] the function is not continuous and if I try and substitute the x and y values into function I end up with [itex]\frac{0}{0}[/itex] and I get similar results if I try [itex]y=mx[/itex]
I have also tried
[itex] \stackrel{lim}{_{x→0}}[/itex] [itex] \frac {(x-1)(x-1+1)y^2}{(x-1+1)^2+y^2}[/itex] and [itex]y=mx[/itex]
Regards
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