Calc III: Section 14.2 Plots
Below we have links to plots constructed by Wolfram Alpha. Feel free to change them and investigate the three dimensional structures.
Exercise 7: (4-xy)/(x^2+3y^2)
Exercise 9: y^4/(x^4+3y^4)
Exercise 11: xycos(y)/(3x^2+y^2)
Exercise 13: xy/sqrt(x^2+y^2)
Exercise 15: x^2ye^y/(x^4+4y^2)
(Hint: See the parabolas in the contour plot?)
Exercise 17: (See text)
(Hint: Recall the technique of multiplying by the conjugate when you see a square root like that?)
Try 23 and 24 on your own (using Wolfram Alpha)
You can try to ask Wolfram Alpha about limits directly.
Here is the limit of x^2+y^2 as (x,y)->(0,0)