2.13.2 Compute lim sups and lim infs for the following sequences (a) {(-1)"n} (b) {sin (nT/8)}...
number 4
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
1. Find 7(5") 3" 5n+12n+1 sin(n!) lim (a) im (b) n 2018 пH0 п2 n oo _ Зп? + п + 4(3") nt T lim sin (d) (с) lim 1 - 2n 3п — 2п n oo n oo 2. Let (an), be a sequence such that lim an n oo L. = 1 (a) What is lm an+1? пH00
number 4 as clearly as possible
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series...
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...
Problem #10: Which of the following sequences converge? (i) an (-1)n+1 n n2 - 7 (-1)" n2 n? - (iii) an = cos(NT) (iv) an= sin(nn) (ii) an= -9 (A) (i) only (B) (ii) only (C) (i) and (iv) only (D) (i) and (iii) only (E) (ii) and (iii) only (F) (ii) and (iv) only (G) all of them (H) none of them
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+
40 Show the following results. 1-e2...
All of the following sequences have end behavior lim an = 0. n>00 Get out a clean sheet of paper. Write down all eight sequences, ordered by the speed at which they go to infinity. After you are done ordering them on paper, order them in WebAssign below. Select 1 for the slowest and 8 for the fastest. 10 n1/4 n In(n) n2n n 100 n! ✓n en?
1. Compute the following limits algebraically, if possible: 4.2 +1-3 (a) lim 5.2 – 1 (b) lim 2 - 2 100 3.42 - 2.c 2 (c) lim csc(7x) sin(4x) (d) lim lim (1+3) 20 22 (e) lim +01 – COS X
8. lim sin? 2x cot4x = .... xoo (A) 1 (B) 4 1 (C) 4 (D) 4 (E)
Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a > 0, . limn-oo a = 0, or a < 0, How does this accord with the various convergence theorems?)
Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a...