(a) By completing the square, show that (b) By factoring x 3 1 as a sum of cubes, rewrite the integral in part (a) Then express 1 (x 3 1) as the sum of a power series and use it to prove the following formula for 1 2 dx x x 1 3 3 Jo...

a b By part a this equals 1 ...

(a) By completing the square, show that (b) By factoring x 3 + 1 as a sum...

Question:

(a) By completing the square, show that

(b) By factoring x³ + 1 as a sum of cubes, rewrite the integral in part (a). Then express 1/(x³ + 1) as the sum of a power series and use it to prove the following formula for π:

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

See More Books

Question Posted: May 20, 2021 06:44 AM

See More Questions

Prove the following formula for a geometric sum 2 ar" = a + ar + ar+ , + ar"- = a, ar"+1
Solve by completing the square to obtain exact solutions. a. x2 + 6x = 7 b. x2 + 8x = -15
ABC Ltd prepares its financial statements to 31 October each year. Its trial balance at 31 October 2019 was as follows: Premises-cost Manufacturing plant-cost Office equipment-cost Accumulated...
The Excel output of a simple linear regression analysis of the data set for this case (see Exercise 13.7 on page 529) is given in Figure 13.14. Recall that a labeled Excel regression output is on...
Many cheeses are produced in the shape of a wheel, and due to manufacturing inconsistencies, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine if...
It looks to me that you have devoted everything to this company and they have treated you badly. Is that right?
An equimolar liquid mixture of benzene and toluene is separated into two product streams by distillation. A process flowchart and a somewhat oversimplified description of what happens in the process...
Define and comprehend the concept of data base and its types. 7. Briefly discuss Database Management Systems. 8. Enumerate and briefly discuss the key concepts of Database Management Systems....
Melissa Young had always been encouraged by her accounting professor to apply her accounting skills as much as possible. When her uncle asked her to prepare his accounting records for a company he...
Give an example of a pair of series a n and b n with positive terms where lim n (a n /b n ) = 0 and b n diverges, but a n converges.
Find the Maclaurin series for f and the associated radius of convergence. You may use either the direct method (definition of a Maclaurin series) or the Maclaurin series listed in Table 11.10.1. f(x)...
Translate the following sentence into a mathematical equation: The total revenue R from selling x hot dogs is $3 times the number of hot dogs sold.
A stock has had returns of -19.6 percent, 29.6 percent, 31.2 percent, -10.7 percent, 35.4 percent, and 27.6 percent over the last six years. What are the arithmetic and geometric returns for the...
Gross Profit Method: Estimation of Fire Loss On September 28, 2016, a fire destroyed the entire merchandise inventory of Carroll Corporation. The following information is available: Sales, January...
Q1. What are the payment amounts of each agreement? Q2. Which forward agreement rate payments should be chosen and why? Q3.What might be the main limitation of the forward rate analysis Forward Rate...
You are a consultant that has been hired to recommend a payout policy for UBT Corp. You have compiled a table with the current tax rates that different types of investors in the stock market face...
You will build a "space" game. We provide "ml-space" as an example to guide you but you may be creative within the restrictions we describe here. Please check the two associated grading rubrics for...
A roller coaster is towed up an incline at a steady speed of 0.50 m/s by a chain parallel to the surface of the incline. The slope is 3.0%, which means that the elevation increases by 3.0 m for every...
Give the structural formulas of the alkenes that, on ozonolysis, give: a. (CH3)2C=O and CH2=O b. Only (CH3CH2)2C=O c. CH3CH=O and CH3CH2CH=O d. O=CHCH2CH2CH2CH=O
Find the directional derivative of f at the given point in the indicated direction. f(x, y, z) = x 2 y + x1 + z, (1, 2, 3), in the direction of v = 2i + j 2k
The second directional derivative of f sx, yd is (a) If u ka, bl is a unit vector and f has continuous second partial derivatives, show that (b) Find the second directional derivative of f sx, yd ...
Find the points on the surface y 2 = 9 + xz that are closest to the origin.
Calculate the limit. lim (9+ h)3-93 h0 h X
The knuckle joint is subject to load P = 12.8 kip. The ultimate shear strength of the pin is 6200 psi. Determine the minimum diameter of the pin.
Instruments in airplane A indicate that, with respect to the air, the plane is headed 30 north of east with an air speed of 340.00 mi/h. At the same time, radar on ship B indicates that the relative...

(a) By completing the square, show that (b) By factoring x 3 + 1 as a sum...

Question:

1/2 dx x? - x +1 3/3 Jo

Step by Step Answer:

a b By part a this equals 1...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions