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Problem 1. Find the following limits. sinn (1) Vn2+1 (2) Vn2 +1. 31 n10 + n2...
3. Find: 7T (1) lim n sin (3) lim arcsin G n-00 n 100 COS- n...
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...
1. Simplify each expression, for n = 5 a) 8n + 2 b) n2 - 2n+n...
1. Simplify each expression, for n = 5 a) 8n + 2 b) n2 - 2n+n d) 19 - 3n + e) (3n - 3) + 15-n-18
2. (28,9) Do the following series converge or diverge? SUPPORT YOUR ANSWERS. You do not have...
2. (28,9) Do the following series converge or diverge? SUPPORT YOUR ANSWERS. You do not have to find the sum. 7n2 - 3n A. Σ ? 2n? +7n +1000 cos(NA) B. IM Vn C. 2*32-
Problem 4. (1 point) Which of the following series converges by the Alternating Series Test? sin(n)...
Problem 4. (1 point) Which of the following series converges by the Alternating Series Test? sin(n) 7n2 00 (-7) 72 B. n1 no 00 C. (-1)"n2 + 7n 2n2 + 10 n1 00 O D. (-1)" 7/n - 3 O E. Both A and B.
Evaluate the following series by applying Parseval's equation to certain of the Fourier expansions in Table...
Evaluate the following series by applying Parseval's equation to
certain of the Fourier expansions in Table 1
10. Evaluate the following series by applying Parseval's equation to certain of the Fourier expansions in Table 1 n2 (n2)2 C. 1 (coth 4 Answer: 7 TABLE 1. FOURIER SERIES 2-1)*! 1. f(0) = 0 (-n <0 < «) sin ne OC 4 cos(2n - 1)e (2n 1)2 2. | f(0) 3D 1Ө| (-п <0 < п) 2 T sin ne (0 0...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's r...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
2. (40 pts) Let fn: RR be given by sin(n) In(x) = n2 NEN. 2a. (10...
2. (40 pts) Let fn: RR be given by sin(n) In(x) = n2 NEN. 2a. (10 pts) Show that the series 2n=1 fn converges uniformly on R. 2b. (10 pts) Show that the function f: RR, f (x) = sin (nx) n2 n=1 is continuous on R. 2c. (10 pts) Show that f given in 2b) is intergrable and $(z)de = 24 (2n-1) 2d. (10 pts) Let 0 <ö< be given. Show that f given in 2b) is differentiable at...
2c. (10 pts) Show that f given in 2b) is intergrable and [ 1 (2) dr...
2c. (10 pts) Show that f given in 2b) is intergrable and [ 1 (2) dr = 2Ě (2n-1) 2d. (10 pts) Let 0 < < be given. Show that f given in 2b) is differentiable at each 1 € (5,27 - 8). Find f' (1). Hint: Use Problem 1 and the following formula In 2 (-1)"-1 Σ 7 n=1 2. (40 pts) Let fn: R → R be given by fn (x) = sin (nx) 3 ηε Ν. n2...
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n...
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n (-1)n+1 loge n (c) (d) 7n + 1 n n=1 n=3 iM: M: Mį M8 sinn (e) ✓n n2 + 2 (f) n2 n=1 n=1 2n en (g) (h) Vn! n=1 n=1
(1) Determine whether the following series converge or diverge: (a) Σ=0 η2 n=1 (b) Σ=0 520...
(1) Determine whether the following series converge or diverge: (a) Σ=0 η2 n=1 (b) Σ=0 520 και (c) Σ=2 /n ln (η) 2n (4) Σ. sin(1) η2 (e) Σ1 (1) Σ=1 n2-3n+1 ln(η).
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...
1. Simplify each expression, for n = 5 a) 8n + 2 b) n2 - 2n+n d) 19 - 3n + e) (3n - 3) + 15-n-18
2. (28,9) Do the following series converge or diverge? SUPPORT YOUR ANSWERS. You do not have to find the sum. 7n2 - 3n A. Σ ? 2n? +7n +1000 cos(NA) B. IM Vn C. 2*32-
Problem 4. (1 point) Which of the following series converges by the Alternating Series Test? sin(n) 7n2 00 (-7) 72 B. n1 no 00 C. (-1)"n2 + 7n 2n2 + 10 n1 00 O D. (-1)" 7/n - 3 O E. Both A and B.
Evaluate the following series by applying Parseval's equation to
certain of the Fourier expansions in Table 1
10. Evaluate the following series by applying Parseval's equation to certain of the Fourier expansions in Table 1 n2 (n2)2 C. 1 (coth 4 Answer: 7 TABLE 1. FOURIER SERIES 2-1)*! 1. f(0) = 0 (-n <0 < «) sin ne OC 4 cos(2n - 1)e (2n 1)2 2. | f(0) 3D 1Ө| (-п <0 < п) 2 T sin ne (0 0...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
2. (40 pts) Let fn: RR be given by sin(n) In(x) = n2 NEN. 2a. (10 pts) Show that the series 2n=1 fn converges uniformly on R. 2b. (10 pts) Show that the function f: RR, f (x) = sin (nx) n2 n=1 is continuous on R. 2c. (10 pts) Show that f given in 2b) is intergrable and $(z)de = 24 (2n-1) 2d. (10 pts) Let 0 <ö< be given. Show that f given in 2b) is differentiable at...
2c. (10 pts) Show that f given in 2b) is intergrable and [ 1 (2) dr = 2Ě (2n-1) 2d. (10 pts) Let 0 < < be given. Show that f given in 2b) is differentiable at each 1 € (5,27 - 8). Find f' (1). Hint: Use Problem 1 and the following formula In 2 (-1)"-1 Σ 7 n=1 2. (40 pts) Let fn: R → R be given by fn (x) = sin (nx) 3 ηε Ν. n2...
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n (-1)n+1 loge n (c) (d) 7n + 1 n n=1 n=3 iM: M: Mį M8 sinn (e) ✓n n2 + 2 (f) n2 n=1 n=1 2n en (g) (h) Vn! n=1 n=1
(1) Determine whether the following series converge or diverge: (a) Σ=0 η2 n=1 (b) Σ=0 520 και (c) Σ=2 /n ln (η) 2n (4) Σ. sin(1) η2 (e) Σ1 (1) Σ=1 n2-3n+1 ln(η).
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