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April 24th, 2012, 12:17 AM  #1 
Newbie Joined: Apr 2012 Posts: 3 Thanks: 0  Define a function z = f(x,y) by f(0,0) = 0 and otherwise
Define a function z = f(x,y) by f(0,0) = 0 and otherwise. f(x,y) =(x^2 y) / (x^2+y^2 ) a. Show that in polar coordinates this function may be expressed (for r? 0) as z = r ?cos?^2 (?)sin(?) b. Show that if ? is fixed then the graph is given by z = mr, a line of slope m= ?cos?^2 (?)sin?(?). (Note that this says that the surface z = f(x,y) is what is called a ruled surface.) c. Compute the directional derivatives of z in the ? direction. Does Df exist at the point (0,0)? Explain. 

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