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% (4 reviews)
a b 511245 X ...View the full answer
Answered By
Mugdha Sisodiya
My self Mugdha Sisodiya from Chhattisgarh India. I have completed my Bachelors degree in 2015 and My Master in Commerce degree in 2016. I am having expertise in Management, Cost and Finance Accounts. Further I have completed my Chartered Accountant and working as a Professional.
Since 2012 I am providing home tutions.
3.30+
2+ Reviews
10+ 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 +...
-
Shemekia applied to a college that uses multiple regression to select students. This college only considers students whose predicted firstyear GPA is 3.0 or higher. Shemekias predicted GPA was 2.9...
-
Suppose the National Foundation for Credit Counseling (NFCC) would like to determine if the median credit card debt for individuals ages 50 years or older exceeds the debt of those younger than 50...
-
When a country specializes in the production of a good, this means that it can produce this good at a lower opportunity cost than its trading partner. Because of this comparative advantage, both...
-
With reference to Exercise 2.12, which pertained to the particle size of cement dust in a factory producing cement, use the sign test at the 0.05 level of significance to test the null hypothesis...
-
Describe in detail all the facets of JetBlues product. What is being exchanged in a JetBlue transaction? In 2007, JetBlue was a thriving young airline with a strong reputation for outstanding...
-
Steam to drive an old-fashioned steam locomotive is supplied at a constant gauge pressure of 1.9110 6 N/m 2 to a piston with a 0.156-m radius. By calculating PV, find the work done by the steam when...
-
In Exercises find a power series for the function, centered at c and determine the interval of convergence. f(x) 1 1 - 3x c=0
-
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
-
Analyze the following independent situations. a. McKinney, Inc. is being sued by a former employee. McKinney believes that there is a remote chance that the employee will win. The employee is suing...
-
How do epistemological paradigms influence the selection and application of Methodology within various fields of inquiry, and what implications do these choices carry for knowledge production?
-
Presented below is information related to Marigold Corp.: Common Stock, $ 1 par $ 3 4 5 0 0 0 0 Paid - in Capital in Excess of ParCommon Stock 5 4 3 0 0 0 Preferred 8 1 / 2 % Stock, $ 5 0 par 2 1 4 0...
-
What role does triangulation play in enhancing the reliability and validity of research findings, and how do researchers integrate multiple sources of data and perspectives within their...
-
Corporate fitness program should always include what two components to ensure attendance adherence and participants success ?
-
Fill in the missing data for each of the following independent cases. (Ignore income taxes.) Note: Do not round intermediate calculations. Leave no cells blank - be certain to enter "O" wherever...
-
Water is sold in bottles that are advertised to contain 1-liter each. Barbara is an inspector for the company and notices that the amount of water in each bottle, unfortunately, has an average of...
-
The executor of Gina Purcells estate has recorded the following information: Assets discovered at death (at fair value): Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
-
Determine the following limits or state that they do not exist. a. b. c. x 4x + 3 lim x2+ (x 2) 2 4 + 3 lim 2 ( 2)2
-
Determine the following limits or state that they do not exist. a. b. c. d. 5x? + 6x .3 lim x-2+ x4 4x2 3 52 + 6 lim x4 - 4x2 > -2
-
Analyze the following limits and find the vertical asymptotes of a. b. c. F(x) x 25 lim f(x) x5*
-
Post a current "marketing in the news" article and evaluate the implications of the event. The article can be a current newspaper, internet, or magazine article about marketing. Please discuss your...
-
One of those macro factors is the competition. For each of the 3 types of competitive advantages, identify a company you believe utilizes that advantage and explain why you believe that to be true....
-
use the information you see below to compose a well written narrative about the customer and their activity depicted below: John Doe Sole Individual check account # 1234567 SSN 123456789 Account...
Study smarter with the SolutionInn App