2n2-31+1 b. lim cos 1. Find the following limits: a. lim 1 00 --- 3n2+4 n-00
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...
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
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c) 4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
Show detailed work 5. (8 points each) Find the limits: V3x2-6 (a) lim X--00 2x -9x (b) lim X-0.x2-sinx COS X (c) lim -X
Un=1 n! Q6-7: Determine whether each series converges conditionally, converges absolutely, or diverges. 1 3n2+4 6. An=1(-1)n-1 7. An=1(-1)n-1 2n2+3n+5 2n2+3n+5 Q8: Compute lim lan+1/an| for the series 2 m2 in Q9: Find the radius and interval of convergence for the series 2n=0 n! 1 Q10: Find a power series representation for (1-x)2 (2-43
3. Find the limits, using L'Hospital's Rule where appropriate. (a) lim 1 - cos (7) 10 (b) lim In (3x + 8) 1+ In (6x + 5) + 10
Find the limits of the following sequences, if they exist. n+ (-1)" COS n An = an = n
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
Find the limit: sin(30) cos(20) lim 00
1. Evaluate each of the following limits: (4 pts ea) b) lim 2- a) lim VF-1 bilim 7-x