Question: Show that for any positive integer n that 1 1 n+1 < In(n + 1) ln(n) < 1/1 n Hint. Obviously, you want to

Show that for any positive integer n that 1 1 n+1 < In(n + 1) ln(n) < 1/1 n Hint. Obviously, you want to use the Mean Value Theorem. See if you can recognize someplace. f(b) - f(a) b-a

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To prove the given inequality using the Mean Value Theorem we consider the function fx lnx According to the Mean Value Theorem if a function f ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Refer to the following PM: Draw a PM that accepts the language UNEQUAL, the complement of EQUAL. READ ADD a a START READ b READ3 b ADD b ACCEPT a

Given the right triangle ABC, which of the following is equal to a/c? I. sinA II. cosB III. tanA A) I only B) II only C) I and II only D) II and III only a b A

Which of the structures shown for the axial conformation of methylcyclohexane do you think is more stable, A or B? Why? A

Nsing the perpetual inventory system, journalize the entries for the following selected transactions: a. b. C. d. Sold merchandise on account, for $12,000, terms n/30. The cost of the merchandise...

T2 with absolute value 1 (namely the eigenvalue 1). Show that if r = is an In eigenvector of A associated with the eigenvalue 1, then _1, * 0. (This result is true even if some eigenvalues of A are...

C# Program In this lab, you will practice the technique of nesting structures, as well as the use of the logical operators, to implement a solution to a slightly more complex problem than those of...

MATH 3210 Practice Final Exam for Discrete I You now have several quizzes and hour exams to study. The following in mainly a repetition of your previous practice and actual exams. 1. (a) Use truth...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Determine what the key terms refer to in the following study. A recent survey by the alumni of a community college indicated that the average salary of its graduates was$37 300, and the average...

In Sample Problem what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles?

The Fair Labor Standards Rot ( FLSA ) deals wath 8 . The amount of Federal Insurance Contributions Act ( FICA ) taxes to be withheld from e - nployear. b . the minimum wage. c . Immigration law. d ....

AI 2 Br s Express your answer as a chemical formula. n

If the net flywheel hp of a tractor engine is 250, what is the estimated PTO hp? O 225 O 278 O 207.5 O 247.5

2. The ester (TM) compound below is useful as a base for perfume. Make a retrosynthetic analysis followed by the synthesis route using the basic ingredients of benzene and 1- butene. COCH3 TM

Calculate the federal income tax using the percentage method for Elida Ledesma who is single with 1 dependent and made $539.90 this weekly pay period. a.) $219.71 b.) $48.86 c.) $40.46 d.) $469.71

B 3 N 3 H 6 . Express your answer as a chemical formula. n

6 Theory of Machines 5. A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and...

Points at which the graphs of r = f() and r = g() intersect must be determined carefully. Solving f() = g() identifies somebut perhaps not allintersection points. The reason is that the curves may...

Find the volume of the solid generated in the following situations. The region R bounded by the graph of y = ln x and the y-axis on the interval 0 y 1 is revolved about the line x = -1.

Let R be the region bounded by the graph of y = sin x and the x-axis on the interval [0, ]. Which is greater, the volume of the solid generated when R is revolved about the x-axis or the y-axis?

Calculate the sums of squares and cross-products, Sxx and Sxy. Find the least-squares line for the data. Plot the points and graph the line on the same graph. Does the line appear to provide a good...

Calculate the sums of squares and cross-products, S xx and S x 16. x 1 3 2 y 6 24

Give the equation and graph for a line with y-intercept and slope given 6. y-intercept = 2.5; slope = 0