Use Theorem 2 to prove that the (x) is represented by its Maclaurin series for all x.
Question:
Use Theorem 2 to prove that the ƒ(x) is represented by its Maclaurin series for all x.
ƒ(x) = sinh x
Transcribed Image Text:
THEOREM 2 Let I = (c-R,c + R), where R > 0, and assume that f is infinitely differentiable on 1. Suppose there exists K> 0 such that all derivatives of f are bounded by K on I: |f(k)(x)| ≤ K Then f is represented by its Taylor series in 1: f(x) = Σ n=0 for all k20 and x = 1 f(n)(c). n! -(x - c)" for all x € I
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (3 reviews)
By definition sinh x 12 e x e x so if both ...View the full answer
Answered By
Ajeet Singh
Professional, Experienced, and Expert tutor who will provide speedy and to-the-point solutions.
I have been teaching students for 5 years now in different subjects and it's truly been one of the most rewarding experiences of my life.
I have also done one-to-one tutoring with 100+ students and help them achieve great subject knowledge.
I have expertise in computer subjects like C++, C, Java, and Python programming and other computer Science related fields.
Many of my student's parents message me that your lessons improved their children's grades and this is the best only thing you want as a teacher. I have done plenty of studying and lots of learning on many exciting and challenging topics. All these experiences have influenced my decision to take on the teaching role in various capacities. As a tutor, I am looking forward to getting to understand your needs and helping you achieve your academic goals. I'm highly flexible and contactable. I am available to work on short notice since I only prefer to work with very small and select groups of students.
4.90+
7+ Reviews
15+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Use Theorem 2 to prove that the (x) is represented by its Maclaurin series for all x. Using Maclaurin series, determine to exactly what value the following series converges: THEOREM 2 Let I = (c-R,c...
-
Use Theorem 2 to prove that the (x) is represented by its Maclaurin series for all x. Using Maclaurin series, determine to exactly what value the following series converges: THEOREM 2 Let I = (c-R,c...
-
Use Theorem 2 to prove that the (x) is represented by its Maclaurin series for all x. (x) = e x THEOREM 2 Let I = (c-R,c + R), where R > 0, and assume that f is infinitely differentiable on 1....
-
Troy Engines, Ltd., manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the carburetors. An...
-
Using the appropriate interest table, answer the following questions. (Each case is independent of the others). (a) What is the future value of 20 periodic payments of $5,000 each made at the...
-
(a) State the Increasing/Decreasing Test. (b) What does it mean to say that f is concave upward on an interval I? (c) State the Concavity Test. (d) What are inflection points? How do you find them?
-
Describe the steps used to develop, execute, and evaluate an advertising program.
-
Alert Medical, LLC, consists of two doctors, Abrams and Lipscomb, who share in all income and losses according to a 2:3 income-sharing ratio. Dr. Lin has been asked to join the LLC. Prior to...
-
The action of account that had previously under the lowance method of acting for collectie Previous Ne O D 944 10/11 DOLL FO FO F10 F11 F12 Priser mert Delete P A $ 4 % 5 1 2 3 & 7 ) 0 Backspace 6 8...
-
Referring to Figure 12, let a be the length of the chord AC of angle of the unit circle. Derive the following approximation for the excess of the arc over the chord: Show that a = 2 sin(/2) and...
-
Let where c is a constant. 00 n=1 c"n! nn
-
In the titration of 10.00 mL of 0.04050 M HCl with 0.01120 M Ba(OH) 2 in the presence of the indicator 2,4-dinitrophenol, the solution changes from colorless to yellow when 17.90 mL of the base has...
-
Consider the following account balances (in thousands) for the Shaker Corporation In the Dec 31.2021 Cash $200,000 and Capital $2,000,000 and Retained earnings $1,500,000 The balances of raw...
-
Unless otherwise stated, assume gravitational acceleration g = 9.81 m/s and the density of water to be 1000 kg/m. Unless otherwise stated, give all numerical answers to 3 significant figures, such as...
-
The purpose of this installment is to classify stock, bond, and mutual fund investments, explore tools for their evaluation and select these securities based on your investment philosophy and goals....
-
Jackson County Senior Services is a nonprofit organization devoted to providing essential services to seniors who live in their own homes within the Jackson County area. Three services are provided...
-
Caldwell (2003) explores differences between the roles of leaders and managers. "Leaders...envision, initiate, or sponsor strategic change of a far-reaching or transformational nature. In contrast,...
-
What are the major changes that are being introduced into UHSMCs?
-
What is beacon marketing? What are digital wallets?
-
Sketch a possible graph of a function f that satisfies all the given conditions. Be sure to identify all vertical and horizontal asymptotes. f(-1) = -2, f(1) = 2, f(0) = 0, = 1, | l lim f(x) lim f(x)...
-
Sketch a possible graph of a function f that satisfies all the given conditions. Be sure to identify all vertical and horizontal asymptotes. lim f(x) = - 00, lim f(x) = 1, = 0, lim f(x) lim f(x) = -2
-
Find the vertical and horizontal asymptotes of f(x) = e 1/x .
-
Docs Auto Body has budgeted the costs of the following repair time and parts activities for 2009: Doc's budgets 6,000 hours of repair time in 2009. A profit margin of $7 per labour hour will be added...
-
QUESTION 28 In a perpetual inventory system, the cost of inventory sold is: Debited to accounts receivable. Debited to cost of goods sold. O Not recorded at the time goods are sold. O Credited to...
-
The following financial statements and additional information are reported. IKIBAN INC. Comparative Balance Sheets June 30, 2019 and 2018 2019 2018 $105,709 69,500 66,800 4,700 246,700 127,eee...
Study smarter with the SolutionInn App