10.1 - Limits

[10.1] - Limits

Try to estimate the following limits by graphing, or by plugging small values for $x$ and $y$ into the appropriate functions. Remember that path independence is important-so try different paths. If the limit exists (or if the limit is $\pm \infty$ ) indicate that. If the limit does not exist, explain why.

5
$+ \infty$ (so DNE)
$- \infty$ (so DNE)
2
0, I think!
I'm trying $y = m x \Rightarrow z = \frac{m^{2} x^{5}}{x^{4} + m x^{8}}$ and all of those look like they approach zero.
This leaves out one approach, along the line $y = 0$ , but if we try that $z = 0 / x^{2}$ , so again it looks like it approaches 0.
Though a surface plot sure looks awful!
0
surface plot of $x^{3} / (x^{2} + y^{2})$
0
as long as we agree to approach only from the first quadrant.
0
surface plot