Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to...

  

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Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to polar coordinates. Use the fact that r0+ as (x, y) (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as ro then the limit does not exist. Second, if there is a function g(r) such that If(r cos(0), r sin(0))| s g(r) for all (r, 0) and lim g(r) = 0, then f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.) lim (x, y)-(0, 0) lim lim (3x+5y3) (x, y) (0, 0) x2 + y (3x+5y3) (x, y)-(0, 0) x2 + y2 7011 6. [-/5 Points] DETAILS MY NOTES A plane lamina occupies the region in the xy-plane between the two circles x2 + y2=4 and x2 + y2 = 64 and above the 00 x-axis. Find the center of mass of the lamina if its mass density is a(x, y) = kg/m. (x-([ Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to polar coordinates. Use the fact that r0+ as (x, y) (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as ro then the limit does not exist. Second, if there is a function g(r) such that If(r cos(0), r sin(0))| s g(r) for all (r, 0) and lim g(r) = 0, then f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.) lim (x, y)-(0, 0) lim lim (3x+5y3) (x, y) (0, 0) x2 + y (3x+5y3) (x, y)-(0, 0) x2 + y2 7011 6. [-/5 Points] DETAILS MY NOTES A plane lamina occupies the region in the xy-plane between the two circles x2 + y2=4 and x2 + y2 = 64 and above the 00 x-axis. Find the center of mass of the lamina if its mass density is a(x, y) = kg/m. (x-([