Transmissions are a work of automotive genius. The transmission takes power from the engine and then multiplies this power through a series of gears to make the car go. When you ha...This calculus 2 video tutorial explains how to find the power series representation of logarithmic functions specifically natural logarithms with ln(1-x^2) a...Introduction to the representation of functions as power series using the geometric series. Examples of how to rewrite and manipulate functions to express th...The power series representation is valid on the interval 1 < f(x) < 1. Here is an example that brings all of this together: Example 1. Find a power series representation for the function 3x2 4+2x3. First, we get a 1 for the constant term in the denominator: 3x2 4 + 2 x3 = 3 x2 4 1 + 1 2 x 3 = 3 4 2 1 + 1 2 3:FlexBook Platform®, FlexBook®, FlexLet® and FlexCard™ are registered trademarks of CK-12 Foundation.Question: Find a power series representation for the function. (Give your power series representation centered at x = 0.) f (x) = ln (5 − x) f (x) = ln (5) − ∞ n = 1. Find a power series representation for the function. (Give your power series representation centered at x = 0.) There are 3 steps to solve this one.Mar 24, 2014 ... Comments110 ; Power series multiplication (KristaKingMath) · 34K views ; Binomial series (KristaKingMath) · 34K views ; Finding radius of convergence...Find a power series representation for \(\frac{1}{1-x^2}\text{.}\) Solution: The secret to finding power series representations for a good many functions is to …1/(1-x)^2=1+2x+3x^2+... We are given f(x)=1/(1-x)^2 This is fairly similar to 1/(1-x), for which we know a power series: 1/(1-x) = 1+x+x^2+...=sum_(k=0)^oo x^k The radius of convergence for this power series is x in (-1,1). While it would be easy to say that 1/(1-x)^2 = (sum_(k=0)^oo x^k)^2 This is not a valid representation of a power series. Usually, some power series arise from derivatives ...Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: Find a power series representation for the function. (Center your power series representation at x = 0.) f (x) = 1/7 + x Determine the interval of convergence. (Enter your answer using interval notation.) Here's the best way to solve it.Your solution's ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. See Answer. Question: Find a power series representation for the function. F (x)= arctan (x/8) sigma _n=1 ^infinity (-1)^n 1/8^2n+1 (2n+1)^x^2n+1 sigma _n=0 ^infinity (-1)^n 1/8^2n+1 (2n+1)^x^2n+1 sigma _n=0 ^ infinity ...Step 1. 3-12 Find a power series representation for the function and determine the interval of convergence. 1 X - 3. f (x)= 4. f (x) = 1 + x 1 + x = 13-14 Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence. 2x - 4 2x + 3 13. f (x) 14. f (x) = = = 2 x² - 4x + 3 2 x² + 3x + 2.Enter a function of x, and a center point a. The widget will compute the power series for your function about a (if possible), and show graphs of the first couple of approximations. Get the free "Power Series" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.Here we discuss power series representations for other types of functions. In particular, we address the following questions: Which functions can be represented by power series and how do we find such representations? If we can find a power series representation for a particular function f f and the series converges on some interval, how do we ...For f(x), find a power series representation centered at the given value of a and determine the radius of convergence. $$ f(x) = \frac {4x} {x^2-2x-3} ; a=0.$$ How would i begin this?See Answer. Question: Find a power series representation for the function. (Center your power series representation at x = 0.) f (x) 1 9 + x f (x) = Determine the interval of convergence. (Enter your answer using interval notation) Find the radius of convergence, R, of the series. x2n n! n=1 R= Find the interval, I, of convergence of the series.I am working through a calc book and one of the problems asks the above question. However, taylor and maclaurin series have not been introduced yet. In some worked examples, they leverage old series, playing it a bit fast and loose with interchanging summation and integration.Question: a)Find a power series representation for the function. f (x) = 4/1 − x9 , n=0 b)Find a power series representation for the function. f (x) = x5/ (9-x2), n=0 c)Find a power series representation for the function f (x) = ln (9 + x2), n=0 d)Evaluate the indefinite integral as a power series. f (x) =integral ( tan−1 (x9) dx), n=0 ...Symbolab is a free online tool that can help you find a power series representation for any function. Enter your function and get step-by-step solutions, explanations and graphs.FlexBook Platform®, FlexBook®, FlexLet® and FlexCard™ are registered trademarks of CK-12 Foundation.A power series about a, or just power series, is any series that can be written in the form, ∞ ∑ n=0cn(x −a)n ∑ n = 0 ∞ c n ( x − a) n. where a a and cn c n are numbers. The cn c n ’s are often called the coefficients of the series. The first thing to notice about a power series is that it is a function of x x.The formula for the value of a geometric series is a/ (1-r), where a is the first term and r is the common ratio. Check out Khan Academy's videos of this. And this indeed means 1/12 is equal to the integral of f (x) from 0 to 1. ( 1 vote)Apr 8, 2021 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...Get four FREE subscriptions included with Chegg Study or Chegg Study Pack, and keep your school days running smoothly. 1. ^ Chegg survey fielded between Sept. 24–Oct 12, 2023 among a random sample of U.S. customers who used Chegg Study or Chegg Study Pack in Q2 2023 and Q3 2023. Respondent base (n=611) among approximately 837K …Get detailed solutions to your math problems with our Power Series step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check …Assuming "power series" is a general topic | Use as referring to a mathematical definition or a calculus result or a word instead. Examples for Series Expansions. Taylor Series. Find a Taylor series expansion: taylor series sin x. Expand around a specified point: series sin x at x=pi/4. Specify the order of the expansion:I am working through a calc book and one of the problems asks the above question. However, taylor and maclaurin series have not been introduced yet. In some worked examples, they leverage old series, playing it a bit fast and loose with interchanging summation and integration.Question: MAC 2312 Worksheet - Section 11.9 5. Find power series representations for the following functions and determine convergence of each inctions and determine the radius of (b) S (:) - tan' (x) (HINT: First find a power series representation for 1/ (1+2).) There are 3 steps to solve this one.Find a power series representation for the functions and determine the intervals of convergence. (a) f(x) = x 2 /(x 4 +16) (b) f(x) = x 2 tan-1 (x 3) There are 2 steps to solve this one. Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Expert-verified.6.1: Power Series and Functions. A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define …FlexBook Platform®, FlexBook®, FlexLet® and FlexCard™ are registered trademarks of CK-12 Foundation.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a power series representation for the function. (Give your power series representation centered at x=0.)Determine the interval of convergence. (Enter your answer using interval notation.)Solution: (1) The function f ( x) is given by. View the full answer Step 2. Unlock. Answer. Unlock. Previous question Next question. Transcribed image text: Find a power series representation for the function. (Give your power series representation centered at x = 0.) f (x) = 1273 Determine the interval of convergence.The problem that was given was to use integration to find a power series representation of the following function $\cosh(\sqrt{x})$. I know how to find the some easy power series representations of something like $\frac{1}{1-x}$ but the $\cosh(\sqrt{x})$ is throwing me off.Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: (a) Find the power series representation of ∫x2ln (1+x2)dx. Be sure to justify your work, including stating the radius of convergence when necessary. (b) Write ∫00.5x2ln (1+x2)dx as an infinite series. There are 2 steps to solve this one.About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...Question: Tutorial Exercise Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.) 1 4 + x Step 1 We need to express f(x) 1 in the form and then use the following equation. 1-1-( 1 - O Step 2 We can re-write f(x) 1 4 + x as Rx) - Step 3 Now, we can use - B=0 f(x) 4+x 1 Xx ^ 4 / 8 − x ^ 3 Find a power series representation for the function; find the interval of convergence. ( Give your power series representation centered at x = 0.) f ( x) = x 4 8 - x 3. ∑ n = 0 ∞ () provided | x | <. There are 2 steps to solve this one.6.1: Power Series and Functions. A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new ...Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: 1) Find a power series representation for the function. (Give your power series representation centered at x = 0.)2)Evaluate the indefinite integral as a power. 1) Find a power series representation for the function.Calculus questions and answers. (a) Use differentiation to find a power series representation for the following function. f (x)1 (6+x) 6n+1 Σ (-1)n (n +1) 6m+3 6m+2 n=2 6m+2 6m+1 What is the radius of convergence? (b) Use part (a) to find a power series for the following function. f (x) = (6+2) CE 6m+2 72 +1 2-0 1) n 1) n 6m+2 n=0 ︵鑑 (-1 ...10.2: Properties of Power Series Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series.Question: Find a power series representation for the function.f (x)=3+x (1-x)2Determine the radius of convergence. Find a power series representation for the function. f ( x) = 3 + x ( 1 - x) 2. Determine the radius of convergence. There are 2 steps to solve this one. Expert-verified.Assuming "power series" is a general topic | Use as referring to a mathematical definition or a calculus result or a word instead. Examples for Series Expansions. Taylor Series. Find a Taylor series expansion: taylor series sin x. Expand around a specified point: series sin x at x=pi/4. Specify the order of the expansion:Find a power series representation for the function. (Give your power series representation centered at x = 0.)g(x) = x4 ln(1 + x)g(x) = \infty n = 1 Evaluate the indefinite integral as a power series.x4 ln(1 + x) dxf(x) = C + \infty n = 1 What is the radius of convergence R?R =10.1: Power Series and Functions. A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define …example 1 Find a power series representation for the function. f(x) = 1 1 − x. The sum of the geometric series. ∑n=0∞ xn = 1 + x +x2 +x3 + ⋯ = 1 1 − x, as long as |x| < 1. Thus, the …Question: 4. (a) Find a power series representation for the function f(x)=3+x1. What is the radius of convergence? (b) Use differentiation and part (a) to find a power series representation for the function g(x)=(3+x)21.Now we know that some functions can be expressed as power series, which look like infinite polynomials. Since calculus, that is, computation of derivatives and antiderivatives, is easy for polynomials, the obvious question is whether the same is true for infinite series. ... Because this is an alternating series with decreasing terms, we know ...This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) x4 f (x) 64 - x3 4+3n x 84 provided |X| < (437) (n! ) (64) n = 0 K.Nov 16, 2022 · Okay, this was the work for the power series representation for \(g\left( x \right)\) let’s now find a power series representation for the original function. All we need to do for this is to multiply the power series representation for \(g\left( x \right)\) by \(x\) and we’ll have it.Mar 28, 2021 ... Learn how to find a power series for a ... Calculus, 11 9 #13 a, Power Series Representation ... Calculus 2 Lecture 9.7: Power Series, Calculus of ...Here’s the best way to solve it. (a) Find a power series representation for the following function. f (x) = ln (1+x) Σ (-1)"-1" O-1 Σ (-1)"-1" o C-1)"3" 27 (134 Σ (-1)"-! What is the radius of convergence? R= (b) Use part (a) to find a power series for the following function. rin (1+x) -1)"."Question: Find a power series representation for the function. f (x) = x3 (x − 2)2 f (x) = ∞ n = 0 Determine the radius of. Find a power series representation for the function. There are 2 steps to solve this one.Find a power series representation centered at 0 for the following function using known power series. Give the interval of convergence for the resulting series. f (x)= ln 121−x2 Which of the following is the power series representation for f (x) ? A. ln11+ 221 ∑k=1∞ 11kx2k B. ln11− 21 ∑k=1∞ 121k⋅kx2k C. ln11− 221 ∑k=1∞ ...Power series of arctan (2x) (video) | Khan Academy. Google Classroom. About. Transcript. We can represent arctan (2x) with a power series by representing its derivative as a …How do you find a power series representation for #(x-2)^n/(n^2) # and what is the radius of... How do you find a power series representation for #f(x)=3/((1-5x)^2)# and what is the radius of... See all questions in Introduction to Power Series Impact of this question. 16232 views around the world ...Exercise 1.2.8. Let V be the volume measure on R2n and hence on Cn. Suppose Δ centered at a ∈ Cn, and f is a function holomorphic on a neighborhood of ¯ Δ. Prove f(a) = 1 V(Δ)∫Δf(ζ)dV(ζ), where V(Δ) is the volume of Δ and dV is the volume measure. That is, f(a) is an average of the values on a polydisc centered at a.Step 1. The given function is, View the full answer Step 2. Unlock. Answer. Unlock. Previous question Next question. Transcribed image text: Find a power series representation for the function. f (y)=ln(11−y11+y) ∑x=0∞ 11x+1(n+1)y2x+1 ∑n−7∞ 2222y2n+1 ∑n=0∞ 11n+1(2n+1)2y2n+1 ∑x=0∞ 11y2x+1 ∑n=0∞ 22y2n+1.Dec 21, 2020 · Recall that . We introduced power series as a type of function, where a value of is given and the sum of a series is returned. Of course, not every series converges. For instance, in part 1 of Example 8.6.1, we recognized the series as a geometric series in . Theorem 60 states that this series converges only when .LEARNING GOAL: to find power series representations (and the corresponding interval & radius of convergence) for functions of the form a1-r using the geometric series theorem from section 10.2.2. For each of the following functions, find a power series representation centered at 0 as well as the corresponding interval & radius ofQuestion: 1. (-/5 Points] DETAILS Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) 1 + x provided x < n = 0 Submit Answer 2. (-15 Points] DETAILS Find a power series representation for the function; find the interval of convergence.Step 1. now the given function is, f ( x) = 5 1 + x Therefore using taylor se... Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x= 0 .) f (x)= 1+x5 ∑n=0∞ (1) provided ∣x∣< -/5 Points] Find a power series representation for the function; find the ...2) Differentiate term by term to get the power series representation of 1 (1 − t)2 1 ( 1 − t) 2. 3) Substitute −3x2 − 3 x 2 everywhere that you see t t in the result of 2). 4) Multiply term by term by x3 x 3. For the radius of convergence, once you have obtained the series, the Ratio Test will do the job.Find a power series representation for the function. (Give your power series representation centered at x = 0.) g (x) = x 3 l n (1 + x) g (x) = ...FlexBook Platform®, FlexBook®, FlexLet® and FlexCard™ are registered trademarks of CK-12 Foundation.Find a power series representation for the function. (Give your power series representation centered at x = 0.)g(x) = x4 ln(1 + x)g(x) = \infty n = 1 Evaluate the indefinite integral as a power series.x4 ln(1 + x) dxf(x) = C + \infty n = 1 What is the radius of convergence R?R =Your solution's ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: Use differentiation to find a power series representation for f (x) = 1/ (6 + x)^2. f (x) = sigmma^infinity_n = 0 () What is the radius of convergence, R? R = Use part (a) to find a power series for f (x) = 1 ...Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: (a) Use differentiation to find a power series representation for the following function. 1 f (0) = (4 + x) . 2n (-1)" (n + 2) 4n+1 n=1 00 Σ (-1)" (n + 1). 4n+2 O 7=2 72 (-1)" (n +1) 4n+2 O n=0 (-1)" (n − 1) 4n+1 n=0 00 ...2 Σ (-1)" (n ...Find power series representations for the following functions about x = a by manipulating known series. State their radius and interval of convergence. Your solution's ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.Question: 4. (a) Find a power series representation for the function f(x)=3+x1. What is the radius of convergence? (b) Use differentiation and part (a) to find a power series representation for the function g(x)=(3+x)21. In 2019, Arthur, the long-running PBS series about an anthropomorphic, school-aged aardvark, aired an e
R = Find a power series representation for f(x) = x2 /(2 + x)3 f(x)= What is the radius of convergence. R? Find a power series representations and radius of convergence. Show transcribed image text. Here’s the best …Calculus questions and answers. Find a power series representation for the function f (y)=ln (1−5y1+5y) 1. f (y)=∑n=1∞2n−1 (−1)n52ny2n−1 (Hint: remember properties of logs.) 2. f (y)=2∑n=1∞2n−1 (−1)n52ny2n−1 3. f (y)=∑n=1∞2n−152n−1y2n−1 4. f (y)=∑n=1∞n1y2n 5. f (y)=∑n=1∞2n−12y2n−1 6. f (y)=2∑n=1∞ ...First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. For example, given the power series representation for f (x) = 1 1−x f ( x) = 1 1 − x, we can find a power series representation for f ′(x) = 1 (1−x)2 f ′ ( x) = 1 ( 1 − ...Enter a function of x, and a center point a. The widget will compute the power series for your function about a (if possible), and show graphs of the first couple of approximations. Get the free "Power Series" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.Learn how to find the power series representation of a function using the Taylor expansion. See examples, key questions, and answers from other users on Socratic.Question: A) Find a power series representation for the function. f (x) = x6 tan−1 (x3) f (x) = ∞ n = 0. A) Find a power series representation for the function. R =? Evaluate the indefinite integral as a power series. ??Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: Find a power series representation for the function. f (x)= x/7x^2 + 1 Determine the interval of convergence. (Enter your answer using interval notation.) There are 2 steps to solve this one.(b) Use part (a) to find a power series representation for f(x) = x3/(3+x)2 Part (a) is Additionally, what is the radius of convergence, R? Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.Now we know that some functions can be expressed as power series, which look like infinite polynomials. Since calculus, that is, computation of derivatives and antiderivatives, is easy for polynomials, the obvious question is whether the same is true for infinite series. ... Because this is an alternating series with decreasing terms, we know ...Find a power series representation (centered at x = 0) and determine the radius and interval of convergence. 0. use differentiation to find a power series representation for 1/(3+x)^2. 1. Power series and partial fractions. 1. Finding convergence center, radius, and interval of power series.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) x4 f (x) 64 - x3 4+3n x 84 provided |X| < (437) (n! ) (64) n = 0 K.Use a power series to represent each of the following functions f f. Find the interval of convergence. f (x) = 1 1+x3 f ( x) = 1 1 + x 3. f (x) = x2 4−x2 f ( x) = x 2 4 − x 2. Show …Question: 4. (a) Find a power series representation for the function f(x)=3+x1. What is the radius of convergence? (b) Use differentiation and part (a) to find a power series representation for the function g(x)=(3+x)21.Use a power series to represent a function. Being able to represent a function by an “infinite polynomial” is a powerful tool. Polynomial functions are the easiest functions to analyze, since they only involve the basic arithmetic operations of addition, subtraction, multiplication, and division. If we can represent a complicated function ...Question: 4. (a) Find a power series representation for the function f(x)=3+x1. What is the radius of convergence? (b) Use differentiation and part (a) to find a power series representation for the function g(x)=(3+x)21.Power Series Representation Problem Hot Network Questions A movie from the 70s, 80s, or 90s like John Carter (2012) with a guy from Earth, a girl, and a caveman/tribesmenJan 24, 2023 ... In this video we begin to express different functions as power series representations. We start with the class of examples relying on the ...He simplified it by subtracting C1 from both sides to get C3 or you can just call it C because you no longer have to differentiate between multiple unknown constants: ln (1 + x³) = C + x³ - ½x⁶ + ⅓x⁹ - ¼x¹². So, when x = 0, we have. ln (1 + 0) = C + 0 - 0 + 0 - 0. which is the same as. ln (1 ) = C + 0 - 0 + 0 - 0.power series solution. en. Related Symbolab blog posts. My Notebook, the Symbolab way. Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back... Enter a problem. Cooking Calculators. Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators.Calculus, Algebra and more at www.blackpenredpen.comDifferential equation, factoring, linear equation, quadratic equation, derivatives, integrals, stewart ca...Calculus questions and answers. (1 point) Book Problem 15 Follow the steps below to find a power series representation for the function f (x) = ln (8 - x): a) A power series for = 1/8+x/64+ (x^2y512 +... (first 3 non-zero terms) 8 - T b) Observe that In (8 - 2) = -1/ (8-x) dx +... (first 3 non-zero c) The function f (x) = In (8 – 2) = terms ...About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...Symbolab is a free online tool that can help you find a power series representation for any function. Enter your function and get step-by-step solutions, explanations and graphs.Integrating power series. Within its interval of convergence, the integral of a power series is the sum of integrals of individual terms: ∫Σf (x)dx=Σ∫f (x)dx. See how this is used to find the integral of a power series.Apr 11, 2021 ... Find power series representation for f(x) = (1+x)/(1-x)^2. Radius of convergence · 11K views ; Power Series - Representation of Functions - ...power series solution. en. Related Symbolab blog posts. My Notebook, the Symbolab way. Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back... Enter a problem. Cooking Calculators. Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators.16x3 (2 − x)3 = ∑n=2∞ n(n − 1)xn+1 2n−2, |x| < 2, (5) (5) 16 x 3 ( 2 − x) 3 = ∑ n = 2 ∞ n ( n − 1) x n + 1 2 n − 2, | x | < 2, or equivalently with a change of indice you get the power series representation. x3 (2 − x)3 =∑n=3∞ (n − 1)(n − 2) xn 2n+1, |x| < 2. (6) (6) x 3 ( 2 − x) 3 = ∑ n = 3 ∞ ( n − 1) ( n ...Question: (a) Use differentiation to find a power series representation for f(x)=(10+x)21f(x)=∑n=0∞( What is the radius of convergence, R?Determine the radius of convergence and interval of convergence of a power series. Use a power series to represent a function. A power series is a type of series …Being able to multiply two power series provides another way of finding power series representations for functions. The way we multiply them is similar to how we multiply polynomials. For example, suppose we want to multiply. ∞ ∑ n=0cnxn = c0 +c1x+c2x2 +⋯ ∑ n = 0 ∞ c n x n = c 0 + c 1 x + c 2 x 2 + ⋯. and.About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...Calculus questions and answers. (1 point) Book Problem 15 Follow the steps below to find a power series representation for the function f (x) = ln (8 - x): a) A power series for = 1/8+x/64+ (x^2y512 +... (first 3 non-zero terms) 8 - T b) Observe that In (8 - 2) = -1/ (8-x) dx +... (first 3 non-zero c) The function f (x) = In (8 – 2) = terms ...Use a power series to represent a function. Being able to represent a function by an "infinite polynomial" is a powerful tool. Polynomial functions are the easiest functions to analyze, since they only involve the basic arithmetic operations of addition, subtraction, multiplication, and division. If we can represent a complicated function ...DO : Work on the following two examples before reading ahead. Example 1: Find a power series representation of the function x 1 + x2 , and determine for which x it would be defined. Example 2 : Find a power series representation of the function 1 7 + 2x, and determine for which x it would be defined. Solution 1: Replace x (in our original f(x ... Use part (a) to find a power series representation for f(x) = x^3/(4 + x)^2. What is the rad