Determine the following limits (if they exist) - (3 points ca 4. lim *-|-x+ 4x4] 14+2...
1. (10 points) Find the following limits, if they exist. a) lim X+2 x 7.-3+ x +3 b) lim XCSCX x → 211
(4) Find the indicated limits, if they exist: (12 points) 5.r-20 1-2 (b) lim- COST (d) lim.--2-5x+6
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
(3) 6 +0 (a) Determine the following limits (if they exist) (1) lim sin 0+tan 36 0 1- (u) lim 1-1 1-3 5 + 3t (11) lim 143 (+3+ 2t2 - 3 (3) (3) (1v) lim 2-2+ (3) -at - bt + ab (v) lam +62 + 2abt - 4202), a, b are real numbers
Evaluate the following limits: x2 +7x - 14 a) lim 2x-5 b) lim tan(3x) - X = c) lim X+0 4x2-3r d) lim a "270 3x - 3xcos(2x) 2x2 sin(3x)
Find the indicated limits if they exist. lim *+0 V1 – 7x-1 x 0
6. Calculate the following limits or determine they don't eadst. (a) (2 points) lim (x,x)=(0,0) + Iniz + y) (b) (2 points)
1. (18 points) Determine if the following limits exist. In each case prove and explain your argument. (a) (c) lim *-(1,5) x+y 4.xy2 2+(0,0) x2 + y2 xy lim (b) x?y2 lim x-(0,0) x4 + 3y
Question 4. Determine (if they exist) the following limits (using l'Hôpital's rule): In(1 + r) - 3 (a) lim (6) (1+r)-1 lim 22 (PER). 10 10 Verify that the assumptions of the theorem on l'Hôpital's rule are satisfied.
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