(a) To prove: Use L'Hopital's rule to prove that for all integers n = 1, lim x → ∞ log b x x 1 / n = 0.

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Answer 1

Question

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

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Pidgeonhole Principle 1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest integer greater than or equal to x. Try figuring out the answers to the following: (a) [2.1] (b) [2] (c) [2.9] (d) [2.1] (e) [2] (f) [2.9] 2. The simple pidgeonhole principle states that, if you have N places and k items (k> N), then at least one hole must have more than one item in it. We tried this with chairs and students: Assume you have N = 12 chairs and k = 18 students. Then at least one chair must have more than one student on it. 3. The general pidgeonhole principle states that, if you have N places and k items, then at least one hole must have [] items or more in it. Try this out with (a) n = 10 chairs and k = 15 students (b) n = 10 chairs and k = 23 students (c) n = 10 chairs and k = 20 students 4. There are 34 problems on these pages, and we…

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The everything combined problem Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server can be active at any time. 1. How many cables would you need to connect each station to each server? 2. How many stations can be used at one time? 3. How many stations can not be used at any one time? 4. How many ways are there to pick 10 stations out of 15? 5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can simultaneously access different servers via direct connections. What is the minimum number of direct connections needed to achieve this goal?

Answer 2

Question

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Answer 6

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

Answer 7

Chapter 11.4, Problem 50ES

To determine

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

Answer 8

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Answer 9

To determine

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Answer 10

Expert Solution & Answer

Answer 11

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Answer 12

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Answer 13

Ch. 11.1 - If f is a real-valued function of a real variable,...Ch. 11.1 - Prob. 2TY Ch. 11.1 - Prob. 3TY Ch. 11.1 - Prob. 4TY Ch. 11.1 - Prob. 5TY Ch. 11.1 - Prob. 6TY Ch. 11.1 - Prob. 1ES Ch. 11.1 - The graph of a function g is shown below. a. Is...Ch. 11.1 - Prob. 3ES Ch. 11.1 - Sketch the graphs of the power functions p3 and p4...

(a) To prove: Use L'Hopital's rule to prove that for all integers n = 1, lim x → ∞ log b x x 1 / n = 0.

Solution Summary: The author explains how to prove that for all integers n = 1, using L'Hopital's rule.

Concept explainers

Videos

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.

Want to see the full answer?

Chapter 11 Solutions

(a) To prove: Use L'Hopital's rule to prove that for all integers n = 1, lim x → ∞ log b x x 1 / n = 0.

Solution Summary: The author explains how to prove that for all integers n = 1, using L'Hopital's rule.

Concept explainers

Videos

(a) To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

(b) Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is O(x1/n) for anyinteger n = 1.

Want to see the full answer?

Chapter 11 Solutions

(a)

To prove: Use L'Hopital's rule to prove that for all integers n = 1, limx→∞logbxx1/n=0.

(b)

Use the result of part (a) and the definitions of limit andof O -notation to prove that logbx is

O(x1/n) for anyinteger n = 1.