Question

lim (x^2(siny)^2)/((7x^2)+(y^2))
(x,y) goes to (0,0)

Answer 1

DNE d/dx=0 d/dy=\[\infty\]

Answer 2

no
I think the right approach is to take the path to (0,0) along y=x http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx