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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. Tags define, function Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post loveinla Calculus 0 April 8th, 2012 12:47 PM Snevk Algebra 18 December 23rd, 2011 01:32 PM Mircode Math Software 0 April 27th, 2011 10:46 PM djon Physics 9 September 15th, 2010 01:43 PM Qer Algebra 1 March 4th, 2010 12:53 PM

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