Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A. Using the definition of limit, show that limn→∞ 1/ n5 = 0 and that limn→∞ 1/ n¹/5 = 0. B. Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ (4 + n) / 2n = 1/2 ii. limn→∞ 2/n + 3/(n+1) = 0 C. Suppose that (sn) and (tn) are sequences so that Sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ Sn = s, then also limn → ∞ tn = S. D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (Sn + tn) is bounded. ii. For any real number a, show that the sequence (a sn) is bounded. E. i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ Sn Za. ii. For each value of a R, give an example of a convergent sequences with sn> a for all n, but where limn→∞ Sn = a.

A. Using the definition of limit, show that limn→∞ 1/ n5 = 0 and that limn→∞ 1/ n¹/5 = 0. B. Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ (4 + n) / 2n = 1/2 ii. limn→∞ 2/n + 3/(n+1) = 0 C. Suppose that (sn) and (tn) are sequences so that Sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ Sn = s, then also limn → ∞ tn = S. D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (Sn + tn) is bounded. ii. For any real number a, show that the sequence (a sn) is bounded. E. i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ Sn Za. ii. For each value of a R, give an example of a convergent sequences with sn> a for all n, but where limn→∞ Sn = a.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.4: Curve Sketching
Problem 32E
See similar textbooks
icon
Related questions
Question
A. Using the definition of limit, show that limn→∞ 1 / n5 = 0 and that limn→∞ 1 / n1/5 = 0. B. Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ (4 + n) / 2n = 1/2 ii. limn→∞ 2/n + 3/(n+1) = 0 C. Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s. D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (sn + tn) is bounded. ii. For any real number α, show that the sequence (α⋅sn) is bounded. E. i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ sn ≥ a. ii. For each value of a ∈ ℝ, give an example of a convergent sequence sn with sn > a for all n, but where limn→∞ sn = a
04:45 hw3 Opened: 5 October 2022, 12.00 AIVI Due: 28 October 2022, 10:00 AM Ė Hw3 - due Oct 28, 10am A. Using the definition of limit, show that limn→∞ 1/ n5 = 0 and that limn→∞ 1/ n¹/5 = 0. B. Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ (4 + n) | 2n = 1/2 ii. limn→∞ 2/n + 3/(n+1) = 0 98 C. Suppose that (sn) and (tn) are sequences so that Sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ Sn = s, then also limn → ∞ tn = S. D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (sn + tn) is bounded. ii. For any real number a, show that the sequence (a sn) is bounded. < Previous activity i Add submission E. i. For a convergent real sequence s, and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ Sna. ii. For each value of a e R, give an example of a convergent sequence sn with sn> a for all n, but where limn→∞ Sn = a. Next activity >
Transcribed Image Text:04:45 hw3 Opened: 5 October 2022, 12.00 AIVI Due: 28 October 2022, 10:00 AM Ė Hw3 - due Oct 28, 10am A. Using the definition of limit, show that limn→∞ 1/ n5 = 0 and that limn→∞ 1/ n¹/5 = 0. B. Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ (4 + n) | 2n = 1/2 ii. limn→∞ 2/n + 3/(n+1) = 0 98 C. Suppose that (sn) and (tn) are sequences so that Sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ Sn = s, then also limn → ∞ tn = S. D. Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i. Show the sequence given by (sn + tn) is bounded. ii. For any real number a, show that the sequence (a sn) is bounded. < Previous activity i Add submission E. i. For a convergent real sequence s, and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ Sna. ii. For each value of a e R, give an example of a convergent sequence sn with sn> a for all n, but where limn→∞ Sn = a. Next activity >
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer