Chapter 4.2, Problem 86E

For the following exercises, evaluate the limit of the function by determining the value the function approaches along the indicated paths. If the limit does not exist, explain why not.

86. ${}_{\left(x,y\right)\to \left(0,0\right)}^{\lim }\frac{xy+y^3}{x^2+y^2}$

a. Along the x-axis(y=0)

b. Along the y-axis(x=0)

c. Along the path y=2x