Question: Show that any positive number M can be represented by (1 + x) / (1 - x), where x lies within the interval of convergence

Show that any positive number M can be represented by (1 + x) / (1 - x), where x lies within the interval of convergence of the series of Problem 11. Hence conclude that the natural logarithm of any positive number can be found by means of this series. Find in 8 this way to three decimal places?

Step by Step Solution

★★★★★

3.38 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If M 1 x 1 x then M Mx 1 x M 1 M 1x x M 1 M 1 M 1 M 1 1 is equivalent to M 1 M 1 M 1 or 0 2M 2M ... 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

Document Format (1 attachment)

955-M-C-D-E (2566).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

We write if for any positive number M there is a corresponding N > 0 such that f(x) > M whenever x > N. Use this definition to prove the following statements. lim f(x) = 00 x- lim xo 100 ||

We write if for any positive number M there is a corresponding N > 0 such that f(x) > M whenever x > N. Use this definition to prove the following statements. lim f(x) = 00 x- .2 lim 00 X-

1. Suppose that a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the 2-year period? (The answer is not 7%) 2. Rework...

Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as...

Please answer question c d e Answer for part a and b Question 3: An Imaginary Floating Point number representation system (16 points) Suppose you are asked to design a 16-bit floating point number...

All info provided Question 3: An Imaginary Floating Point number representation system (16 points) Suppose you are asked to design a 16-bit floating point number system that works in a similar way as...

Question 3: An Imaginary Floating Point number representation system (16 points) Suppose you are asked to design a 16-bit floating point number system that works in a similar way as the IEEE754...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

Air flows steadily through an adiabatic turbine, entering at 150 psia, 900oF, and 350 ft/s and leaving at 20 psia, 300oF, and 700 ft/s. The inlet area of the turbine is 0.1 ft2. Determine (a) The...

Increases or decreases in the riskiness of the future value of an asset have interesting and important effects on the value of call and put options written on the property today. To illustrate this,...

10. What evidence is necessary to demonstrate the ability to defer settlement of short-term debt?

According to an article in The Economist, citizens of the United States consider college to be the best investment in the country. However, this view is based on broad averages, which obscure the...

Glucose production as a function of mass. Estimate glucose production when the mass reaches 20.0 g. Graph the following relations between measurements of a growing plant, checking that the points lie...

The line f(x) = 2x + 3 and the point (2, 7). Check that the point indicated lies on the line and find the equation of the line in point-slope form using the given point. Multiply out to check that...

Volume as a function of mass. Estimate the volume when the mass reaches 30.0 g. How will the density at that time compare with the density when a = 0.5? Graph the following relations between...

Grade-point averages. Find the mean and median for the grouped data in the following table. Interval 1.952.15 2.152.35 2.352.55 2.552.75 2.752.95 2.953.15 3.153.35 3.353.55 3.553.75 3.753.95...

You have $20,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 15 percent and Stock Y with an expected return of 8 percent. (a) If your goal is to create a...

Give the correct answer with detailed explanation and don't copy from internet. ? chapter 10 (Two populations, hypothesis) @ Saved Help Sa 2 b-2. Find the p-value. 171 Op-value