[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.

  1. 5
  2. $+\infty$ (so DNE)
  3. $-\infty$ (so DNE)
  4. 2
  5. 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!

  6. 0

    surface plot of $x^3/(x^2+y^2)$

  7. 0

    as long as we agree to approach only from the first quadrant.

  8. 0

    surface plot