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Exercise 2. cosh (3z/2) (a) Show that 2 cosh(#) -1= cosh (z/2) (-) 2 cosh (b) Calculate lim n-+00 3k Exercise...
Thank you! Exercise 33: (How good are your integration skills?) Let m E N. Show that 2772)! (ech()a π 2m+1 and cosh(...
Thank you!
Exercise 33: (How good are your integration skills?) Let m E N. Show that 2772)! (ech()a π 2m+1 and cosh(z) = 2e+ e-*), x E R. (z) = cosh(x) a) Make a change of variables such that 0 Hint: You may use that sech : [0.00) → (0, 1] is invertible with-sech-1(r) b) Make a change of variables such that c) Show that π 2772)! 2ml :- (2mm!)2 2 To do so, you may show that m- PrL...
2n2-31+1 b. lim cos 1. Find the following limits: a. lim 1 00 --- 3n2+4 n-00
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...
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. n-00 n
2. Prove that lim (-1)"+1 = 0. n-00 n
Which of the following statements is correct? lim " = 0o, ne z 00 1 lim...
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
2. Prove that lim (-1)"+1 0. 72-00 n 2n 3. Prove that lim noon + 1...
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
Exercise 15: Let (cn) be a sequence of positive numbers. Prove: lim infºn+1 < lim infch/n....
Exercise 15: Let (cn) be a sequence of positive numbers. Prove: lim infºn+1 < lim infch/n. n700 Cnn +00 What is the corresponding inequality for the lim sup?
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the...
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
x-4 a) lim x-2 X-2 xe* b) lim *-01-et lim (1+x)'* X+00
x-4 a) lim x-2 X-2 xe* b) lim *-01-et lim (1+x)'* X+00
(2) Let r1 1 and -(-) 1 (n+1)2 = I+ur (a) Show that lim,, T, exists....
(2) Let r1 1 and -(-) 1 (n+1)2 = I+ur (a) Show that lim,, T, exists. (b) Prove that z, #t1 by induction and find the limit.
Thank you!
Exercise 33: (How good are your integration skills?) Let m E N. Show that 2772)! (ech()a π 2m+1 and cosh(z) = 2e+ e-*), x E R. (z) = cosh(x) a) Make a change of variables such that 0 Hint: You may use that sech : [0.00) → (0, 1] is invertible with-sech-1(r) b) Make a change of variables such that c) Show that π 2772)! 2ml :- (2mm!)2 2 To do so, you may show that m- PrL...
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...
2. Prove that lim (-1)"+1 = 0. n-00 n
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
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
Exercise 15: Let (cn) be a sequence of positive numbers. Prove: lim infºn+1 < lim infch/n. n700 Cnn +00 What is the corresponding inequality for the lim sup?
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
x-4 a) lim x-2 X-2 xe* b) lim *-01-et lim (1+x)'* X+00
(2) Let r1 1 and -(-) 1 (n+1)2 = I+ur (a) Show that lim,, T, exists. (b) Prove that z, #t1 by induction and find the limit.
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