1. (18 points) Determine if the following limits exist. In each case prove and explain your...
1. (18 points) Determine if the following limits exist. In each case prove and explain your argument. (a) (0) lim ху 4xy? 2+(1,5) x+y lim **(0,0) x2 + y2 (b) x²y² lim *-*(0,0) *4 + 3y 2 (14 neinte) Find the derivative hole
=) Determine if the following limits exist. In each case prove and explain your argument. (c) xy lim *+(1,5) x + y 4xy2 lim *-*(0,0) x2 + y2 lim x²y² *+(0,0) x4 + 3y4
1. Determine if the following limits exist. In each case prove and explain your argument. (a) lim x+y + xy sin x siny x²y lim *+(0,0) x4 + y2 x(0,0) xy
1. Determine if the following limits exist. In each case prove and explain your argument. (c) lim x +y + y sin x siny *(0,0) XY lim x-(0,0) x4 + y2 lim x+(0,0) x2y2 + (x + y2)2
please compute these two limits, or explain why they dont
exist
(2x - 2)y lim (x,y)+(1,0) (x - 1)2 + y2 xy2 lim (1,y)+(0,0) x2 + y2
help me. ASAP
2. Show that the following limits do not exist 1.2. Limits and Continuity (a) lim(x,y)=(0,0) DEO (b) lim(x,y)=(0,0) 2,2*-*y2 (c) lim (2,3)+(0,0) 4x2-2y2 n(x,y)+(0,0) x2 - 3y2
2.c)
2. Show that each of the following limits does not exist : (a) lim 1 + 2y (b) lim (2 + y) (x,y)--(0,0) -y (2.) +0,0) r? + y2 (d) 6ry lim (x,y)+(0,0) 24 + y (c) lim (x,y)0,0) - 2 + y
(4) Evaluate each of the following limits or show that the limit does not exist: (a lim 2014 – 2y4 (3,4) (0,0) 22 - y2 lim 1 + 2y (x,y) (0,0) = -2y (b)
1. Sketch a few of the level curves of the function f(x, y) = surface z = y2 and then use these to graph the f (x, y) 2. Evaluate the following limits if they exist. If they don't, explain why not. (a lim (x,y)(0,0) + 4y2 x4-y4 (b lim (x,y)(0,0) x2 + y2 cos 2 y2) - 1 lim (c (z,y)(0,0 2ry (x, y)(0,0) Is the function f(x, y) continuous at (0,0)? 3 = (х, у) — (0,0) 2x2y...
3. (5 pts. each) Evaluate the following limits if they exist. If the limit does not exist, then use the Two-Path Test to show that it does not exist. 5x²y (a) lim (x,y)=(0,0) **+3y2 (b) lim (x,y)-(1,-1) 1+xyz