In Exercises find a geometric power series for the function, centered at 0 (a) By the technique
Question:
In Exercises find a geometric power series for the function, centered at 0
(a) By the technique shown in Examples 1
(b) By long division
Data from in Examples 1
Transcribed Image Text:
Long Division 2 x + x²x²³+. 2 + x) 4 4 + 2x -2x -2x - x² x² x² + x³² đ EXAMPLE 1 Finding a Geometric Power Series Centered at 0 Find a power series for f(x): 4 x + 2' Solution Writing f(x) in the form a/(1-r) produces 4 2 1-(-x/2) 2 + x which implies that a = 2 and r = = X So, the power series for f(x) is 4 x + 2 = = 00 n=0 00 ar" = 11 a A=0 = 2(1 – This power series converges when centered at 0. . ) which implies that the interval of convergence is (-2,2). Another way to determine a power series for a rational function such as the one in Example 1 is to use long division. For instance, by dividing 2 + x into 4, you obtain the result shown at the left.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (10 reviews)
a b 1 2 x 12 ...View the full answer
Answered By
Asim farooq
I have done MS finance and expertise in the field of Accounting, finance, cost accounting, security analysis and portfolio management and management, MS office is at my fingertips, I want my client to take advantage of my practical knowledge. I have been mentoring my client on a freelancer website from last two years, Currently I am working in Telecom company as a financial analyst and before that working as an accountant with Pepsi for one year. I also join a nonprofit organization as a finance assistant to my job duties are making payment to client after tax calculation, I have started my professional career from teaching I was teaching to a master's level student for two years in the evening.
My Expert Service
Financial accounting, Financial management, Cost accounting, Human resource management, Business communication and report writing. Financial accounting : • Journal entries • Financial statements including balance sheet, Profit & Loss account, Cash flow statement • Adjustment entries • Ratio analysis • Accounting concepts • Single entry accounting • Double entry accounting • Bills of exchange • Bank reconciliation statements Cost accounting : • Budgeting • Job order costing • Process costing • Cost of goods sold Financial management : • Capital budgeting • Net Present Value (NPV) • Internal Rate of Return (IRR) • Payback period • Discounted cash flows • Financial analysis • Capital assets pricing model • Simple interest, Compound interest & annuities
4.40+
65+ Reviews
86+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
In Exercises find a geometric power series for the function, centered at 0 (a) By the technique shown in Examples 1 (b) By long division Data from in Examples 1 Long Division 2 x + xx+. 2 + x) 4 4 +...
-
In Exercises find a geometric power series for the function, centered at 0 (a) By the technique shown in Examples 1 (b) By long division Data from in Examples 1 Long Division 2 x + xx+. 2 + x) 4 4 +...
-
In Exercises find a geometric power series for the function, centered at 0 (a) By the technique shown in Examples 1 (b) By long division Data from in Examples 1 Long Division 2 x + xx+. 2 + x) 4 4 +...
-
An investor has $60,000 to invest in a $280,000 property. He can obtain either a $220,000 loan at 9.5 percent for 20 years or a $180,000 loan at 9 percent for 20 years and a second mortgage for...
-
Consider the following data from two independent samples: Perform a hypothesis test using α = 0.05 to determine if the population from which Sample B was drawn has a higher median than...
-
All birds, independent of their size, must maintain a power output of 10-25 watts per kilogram of body mass in order to fly by flapping their wings. (a) The Andean giant hummingbird (Patagona gigas)...
-
Performers in the Rock and Roll Hall of Fame From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals, and 206 of the inductees have been performers while...
-
A firm produces a perishable food product at a cost of $10 per case. The product sells for $15 per case. For planning purposes, the company is considering possible demands of 100, 200, and 300 cases....
-
How do circular economy principles and reverse logistics systems optimize resource utilization and minimize waste generation throughout the product lifecycle, promoting sustainable consumption...
-
In Exercises find a power series for the function, centered at c and determine the interval of convergence. f(x) 2 6 - x' C = -2
-
In Exercises explain how to use the geometric series to find the series for the function. Do not find the series. g(x) = 1 1- x =x", |x| < 1 n=0 =
-
As the manager of a call centre, what would you want your staff to do in such circumstances, and why?
-
Can you help me solve this using this data and make the path length =0.05 Part II. Ferrichrome A. Your TA will give you a solution of unknown concentration of ferrichrome A. From its millimolar...
-
*(f) The infrared spectrum of this unknown shows a strong peak near 1715 cm. Relative Abundance 100 80- 60 40- 20- 43 72 L 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130...
-
Subang to thogong boyredo ne TO el gubwollo) sa zoban visart 5. The analysis of a rocket fuel showed that it contained 87.4% nitrogen and 12.6% hydrogen by weight. The fuel's molar mass was...
-
Match the protective material with each nuclide. Paper 5 mm aluminum 10 cm lead A BO 99m Tc 222 Rn 32p
-
Five standard iron solutions were prepared, and the absorbance of the solutions were measured using a spectrophotometer. The table below gives concentrations of iron ( [ Fe ] in g M L ) and their...
-
Kimiko signed a loan agreement requiring payments of $234.60 at the end of every month for six years at 7.2% compounded monthly. (a) How much was the original loan balance? (b) If Kimiko missed the...
-
Explain briefly what is meant by electronic data interchange (EDI). How does EDI affect a companys audit trail?
-
Graph the function y = tan x with the window [-, ] [-10, 10]. Use the graph to analyze the following limits. a. b. c. d. tan x lim xn/2+ X- lim tan x - xn/2
-
Determine the following limits or state that they do not exist. 3 lim 0 -5? 5x2
-
Determine the following limits or state that they do not exist. 412 100 lim 5
-
The (2 x 2) matrices listed in Eq. (9) are used in several of the exercises that follow. A = 2 = [ } } ] 2 3 c-[ 7 } ] = 1 1 B Z = 0 - 1 3 00 z=[% % ] 00 Exercises 1-6 refer to the matrices in Eq....
-
Given: R = 20x and C = (10x300, x < 20 10x+250, x 20 1. Find the break-even point or points, if any. 2. Graph these results (be sure to label "completely")
-
Prepare the journal entry to record the payment of interest and the discount amortisation on December 3 1 , 2 0 2 2
Study smarter with the SolutionInn App