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) = e−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: 0% (1 review)
For any c choose any R 0 and consider the interval c ...View the full answer
Answered By
Khurram shahzad
I am an experienced tutor and have more than 7 years’ experience in the field of tutoring. My areas of expertise are Technology, statistics tasks I also tutor in Social Sciences, Humanities, Marketing, Project Management, Geology, Earth Sciences, Life Sciences, Computer Sciences, Physics, Psychology, Law Engineering, Media Studies, IR and many others.
I have been writing blogs, Tech news article, and listicles for American and UK based websites.
4.90+
5+ Reviews
17+ 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) = sinh x THEOREM 2 Let I = (c-R,c + R), where R > 0, and assume that f is infinitely differentiable on 1....
-
$ 45.00 Direct material: 5 pounds at $9.00 per pound Direct labor: 3 hours at $14 per hour Variable overhead: 3 hours at $9 per hour Total standard variable cost per unit 42.00 27.00 $114.00 The...
-
Maria Alvarez is investing $300,000 in a fund that earns 8% interest compounded annually. What equal amounts can Maria withdraw at the end of each of the next 20 years?
-
In Exercises match the function with one of the graphs [(a), (b), (c), (d), (e), or (f)] using horizontal asymptotes as an aid. (a) (b) (c) (d) (e) (f) -2 -1 3 -1 1 2 X
-
(a) A rectangular loop of wire is \(\ell=800 \mathrm{~mm}\) long and \(w=500 \mathrm{~mm}\) wide. You bend the \(\ell\) sides into a semicircle while keeping the \(w\) sides straight, as shown in...
-
A. H. Zehmer discussed selling a farm to Lucy. After a 40-minute discussion of the first draft of a contract, Zehmer and his wife, Ida, signed a second draft stating: We hereby agree to sell to W. O....
-
We have defined a PyTorch network class DAN for you. You need to implement the forward pass for your deep averaging network. To start, first implement average that averages the words in a review and...
-
Show that the Ratio Test does not apply, but verify convergence using the Direct Comparison Test for the series 1 1 + 2 32 + 1 23 + 1 34 + 1 25 +
-
Use the appropriate limit laws and theorems to determine the limit of the sequence or show that it diverges. an = 3-4" 2+7.3n
-
Refer to Exercise 10.21. Find a 99% confidence interval for (µ1 - µ2). Exercise 10.21 Independent random samples of n1 = 16 and n2 = 13 observations were selected from two normal...
-
For this problem a 2d array of ints represents the value of each block in a city. Each element in the array is a city block. The value of a block could be negative indicating the block is a liability...
-
Thw case is from an Introduction to Finance Course at the Smith School of Business (COMM 121): WEIGHTED AVERAGE COST OF CAPITAL (FALL 2023): BOMBARDIER Shin Lee, a commerce student at the Smith...
-
------------------------------------------------------------------------------------------------------------ 1. Think of a client / website. A small to medium size company. Which website did you...
-
The advertising budgets of small stores in Los Angeles is normally distributed with a mean of $5,400 and a standard deviation of $2,100. What percentage of small stores in L.A. have an advertising...
-
From your analysis, you understand that the net margin for the organization has shown strong growth over the past year. What factor/s is/are driving this improved performance? What concerns do you...
-
The data shown here, from the Investment Company Institute, show that the equity fund assets of mutual funds have been growing since 1981. At the same time, money market funds have been increasing...
-
Below is a sample of the data in the file NFLAttendance which contains the 32 teams in the National Football League, their conference affiliation, their division, and their average home attendance....
-
Use Theorem 2.10 to determine the intervals on which the following functions are continuous. p(x) = 4x 5 - 3x 2 + 1
-
Use Theorem 2.10 to determine the intervals on which the following functions are continuous. 3x2 6x + 7 2 8(x) x + x + 1 .2
-
Use Theorem 2.10 to determine the intervals on which the following functions are continuous. x' + 6x + 17 x 9 f(x)
-
On March 1, Year 1, Justis, LLP bought and classified the 10-year debt investments detailed below as available-for-sales ear 1, justis is preparing its financial statements for the end of the fiscal...
-
Tent Master produces Pup tents and Pop-up tents. The company budgets $255,000 of overhead cost and 51,000 direct labor hours. Additional information follows. Per Unit Pup tent Selling Price $ 80...
-
Beretta, Inc. has outstanding 500,000 shares of $13.00 par value common stock. Ruger declares a 7.75% stock dividend at $17.00 per share. What will be the amount recorded to the Retained Earnings...
Study smarter with the SolutionInn App