[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 $y=mx\Rightarrow z=\frac{m^2x^5}{x^4+mx^8}$ 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
- 0
as long as we agree to approach only from the first quadrant.
- 0