100 1. (a) (3 pt) Find the value of A such that lim (Vn? + (24 – 1)n +1 – Vn? +2n) = 0. (b) (3 pt) Find the value of B such that lim (Vn* – 5Bn2 +1 – Vnd – (B+ 2)/2) = 1200
9-24 Evaluate the limit, if it exists. 2 - 6x + 5 9. lim 10_lim x² - 4x 3-4 x - 5 why. - 5x4+ 6 -5 2r² + 3xunt 12. lim 1-1 r2 - 2x 13. lim 21,7t + 3 14. lim -182 - 3x - 4 4 + 12 – 16 15 lim 16. lim h 0 (2 + h): - 8 h 1 + 1 - 1 h 17. lim -27 + 8 18. lim h 0
Find the following: z2+9 e) lim 23į 2-3i z2+i f) lim 2-i 24-1 Write given numbers in the polar form reio: 3 a) (cos 29 + i sin 27)
. x2 + 2x – 8 Find lim *2 X – 2 For DNE, enter 100 as your answer. Answer:
16. lim n-> inf 24. Find the limit of the sequence 25. lim n-> inf . limit= We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
(1 point) Evaluate the limit lim vz? +6x +5 - 2 100
m2 2. Prove that lim -+0n3 + 1 -=0. 3 5 100 3n2 + 2n - 1 3. Prove that lim = 5n2 +8 cos(n) 4. Prove that lim = 0. n-700 m2 + 17 5. Prove that lim (Vn+1 - Vn) = 0 Hint: Multiply Vn+1-vñ by 1 in a useful way. In particular, multiply Vn+1-17 by Vn+1+vn
3. Find: 7T (1) lim n sin (3) lim arcsin G n-00 n 100 COS- n n00 n 1 (4) lim (1+ (6) lim (n+1 n) n- 3n n-00 1/n (2) lim arctann Vn2 - 1 (5) lim 2n In (1+) (8) lim n (11) lim n+ n 2+1 (14) lim n- 75n+2 (9) lim (nt n-00 700 n->00 n (7) lim V (Vn+1- Vn) (-1)"n (10) lim n+ on+1 (13) lim (3" +5")1/n sinn (12) lim arctan 2n 2n...
2. Evaluate the following limits. a) lim Vr+6-2 23 23 – 3.22 b) lim th h c) lim 3(2-2) cos(3) 22 +62 +9 h0 100
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