My Math Forum Define a function z = f(x,y) by f(0,0) = 0 and otherwise

 Real Analysis Real Analysis Math Forum

 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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top