(4) Find the indicated limits, if they exist: (12 points) 5.r-20 1-2 (b) lim- COST (d)...
Determine the following limits (if they exist) - (3 points ca 4. lim *-|-x+ 4x4] 14+2 --- 5. lim √5 - x-5 √x-5 6. lim-7x-12
Find the indicated limits if they exist. lim *+0 V1 – 7x-1 x 0
1. (10 points) Find the following limits, if they exist. a) lim X+2 x 7.-3+ x +3 b) lim XCSCX x → 211
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
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.
f(x) 12. If lim z = 5, find the following limits. (m) lim f(x) (b) lim
5. (8 points each) Find the limits: V3x2-6 (a) lim X-00 2x -9X (b) lim x=0x2-sinx COS X (c) lim x X- 2 2
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
2. Find the limits of the following functions if they exist. Show all necessary work. If the limit is co or -00, then state this rather than that it does not exist: (2 points each) a. lim x+3 V6x-2-4 x-3 b. lim arctan(3x) x sin(x) 3. Find the average value of the function f(x) = 4x2 + 8x -1 on (-1, 3).
find the limits analytically, show all steps x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....