which of the following integrals equals:
which of the following integrals equals: Question: Which of the following integrals equals lim n-00 2n...
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. Prove that lim (-1)"+1 0. 72-00 n 2n 3. Prove that lim noon + 1 2. 80 4. Prove that lim n-+v5n 0. -7 9 - in 5. Prove that lim n0 8 + 13n 13
2n2-31+1 b. lim cos 1. Find the following limits: a. lim 1 00 --- 3n2+4 n-00
Which of the following statements is correct? lim " = 0o, ne z 00 1 lim 1+2 0,nez olim r" = -00, NEN 100 Olim 2-" = 0, neN 100
n+00 1. A series an has the property that lim an = 0. Which of the following is true? n=1 (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (d) There is not enough information to determine whether the series converges or diverges.
For the following sums write down the corresponding integrals: N i 00 1 100 /3+ 0.1 . i . 0.05i e) For the following sums write down the corresponding integrals: N i 00 1 100 /3+ 0.1 . i . 0.05i e)
2 6 Ine 1 Question 7 1 pts Which of the following integrals is equivalent to ' V1 - 22 •da 2 None of these sec (0) dᎾ tan(0) Ś tan? (0)do cos? (0) dᎾ L'ava Vudu Question 8 1 pts
1. A series has the property that lim an = 0. Which of the following is true? (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (a) There is not enough information to determine whether the series converges or diverges. 1 n-00 2 2. A sequence {sn} of partial sums of the series an has the property that lim sn Which of the...
solve a and c only 1. Use the residue theorem to evaluate the following integrals: cos θ (2+sin θ) 2n 0 0 1+sin2 θ 2x-0820, de (C) Jo 5-4cos
We have the following Limit Comparison Test for improper integrals: Theorem. Suppose f(x), g(x) are two positive, decreasing functions on all x > 1, and that lim f(x) =c70 x+oo g(x) Then, roo 5° f(x) dx < oo if and only if ſº g(x) dx < 00 J1 (a) Using appropriate convergence tests for series, prove the Limit Comparison Test for improper integrals. (Hint: Define two sequences an = f(n), bn = g(n). What can you say about the limit...