Chapter 4.2, Problem 88E

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.

87. Evaluate ${}_{\left(x,y\right)\to \left(0,0\right)}^{\lim }\frac{xy+y^3}{x^2+y^2}$ using the results of previous problem.

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

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

c. Along the path y=2x