Explanation Given: The increasing growth rate of the sequences { a n } ≪ { b n } . Theorem used: Growth Rates of Sequences If the increasing growth rate of the sequence { a n } appears before { b n } as n → ∞ , then lim n → ∞ a n b n = 0 and lim n → ∞ b n a n = ∞ . The increasing growth rate of the sequences are { n ! } ≪ { n n } . Proof: Consider the sequences { a n } ≪ { b n } . Thus, by Result stated above lim n → ∞ a n b n = 0

Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)

2nd Edition

ISBN: 9780321977298

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 8.2, Problem 104E

To determine

To prove: The increasing growth rate {can}≪{dbn} where c and d are positive real numbers.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 103E

Chapter 8.2, Problem 105E

Students have asked these similar questions

An object of mass 4 kg is given an initial downward velocity of 60 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is - 8v, where v is the velocity of the object in m/sec. Determine the equation of motion of the object. If the object is initially 500 m above the ground, determine when the object will strike the ground. Assume that the acceleration due to gravity is 9.81 m/sec² and let x(t) represent the distance the object has fallen in t seconds. Determine the equation of motion of the object. x(t) = (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.)

Early Monday morning, the temperature in the lecture hall has fallen to 40°F, the same as the temperature outside. At 7:00 A.M., the janitor turns on the furnace with the thermostat set at 72°F. The time constant for the building is = 3 hr and that for the building along with its heating system is 1 K A.M.? When will the temperature inside the hall reach 71°F? 1 = 1 hr. Assuming that the outside temperature remains constant, what will be the temperature inside the lecture hall at 8:30 2 At 8:30 A.M., the temperature inside the lecture hall will be about (Round to the nearest tenth as needed.) 1°F.

Find the maximum volume of a rectangular box whose surface area is 1500 cm² and whose total edge length is 200 cm. cm³

Chapter 8 Solutions

Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To prove: The increasing growth rate { c a n } ≪ { d b n } where c and d are positive real numbers.

Solution Summary: The author analyzes the increasing growth rate of the sequences leftca_nrightll and inftymathrmlim

Concept explainers

Videos

To prove: The increasing growth rate {can}≪{dbn} where c and d are positive real numbers.

Want to see the full answer?

Chapter 8 Solutions