Let E(x) = k=0 xk/k!. a) Prove that the series defining E(x) converges uniformly on any closed
Question:
a) Prove that the series defining E(x) converges uniformly on any closed interval [a, b].
b) Prove that
for all a, b R.
c) Prove that the function y = E(x) satisfies the initial value problem
y'-y = 0, y(0 ) = l.
[We shall see in Section 7.4 that E(x) = ex.]
Transcribed Image Text:
la E(x) dx = E(b)-E(a)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 60% (10 reviews)
a Since x k1 k 1x k k xk 1 0 as k this series converges point wise on R by the Ratio Tes...View the full answer
Answered By
Joseph Njoroge
I am a professional tutor with more than six years of experience. I have helped thousands of students to achieve their academic goals. My primary objectives as a tutor is to ensure that students do not have problems while tackling their academic problems.
4.90+
10+ Reviews
27+ Question Solved
Related Book For
Question Posted:
Students also viewed these Numerical Analysis questions
-
Suppose that ak I 0 as k . Prove that k=1 ak sin kx converges uniformly on any closed interval [a, b] (0, 2).
-
Prove that (1 - x/k)k e-x uniformly on any closed, bounded subset of R.
-
Prove that the geometric series converges uniformly on any closed interval [a, b] (-1, 1). 1L:
-
What effect does a weakening in U.S dollar have on Net Income for subsidiaries of U.S companies?
-
Your parents have accumulated a $120,000 nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Courtney. However, Courtney has decided to...
-
Costco Wholesale Corporation owns and operates membership warehouses in the United States, Canada, United Kingdom, Mexico, Japan, Korea, Australia, Spain, France, and Iceland. Costco also engages in...
-
DuPont's Web site (www.dupont.com) shows 13 market sectors in which DuPont sells its products. Prepare a table similar to Table 1.2 in which the chemical products are classified by industrial sector...
-
Alternative denominator-level capacity concepts effect on operating income. Lucky Lager has just purchased the Austin Brewery. The brewery is two years old and uses absorption costing. It will sell...
-
a- What is the output of implementing the class Entity2 in the following code class Entity1 { public Entity1() { } System.out.println("Entity1's no-arg constructor is invoked"); } class Entity3...
-
Lawn King manufactures two types of riding lawn mowers. One is a low-cost mower sold primarily to residential home owners; the other is an industrial model sold to landscaping and lawn service...
-
Suppose that f1, f2,... are continuous real functions defined on a closed, bounded interval [a, b]. If 0 1/n [ro) dx = | fw) dx. lim %3D1
-
Suppose that Prove that cos(kx) f(x) = .
-
A new coffee shop opens and to maximize profit it hires 5 workers at the competitive wage rate. The price of a cup of coffee is $4 and the value of marginal product of workers in the coffee shop is...
-
23. Write a C program that reads three floating values and check if it is possible to make a triangle with them. Also calculate the perimeter of the triangle if the said values are valid. Go to the...
-
(A) Discuss the connections and differences between partitional clustering and hierarchical clustering. (B) Explain self-organizing map and its "topology preserving properties". (C) Training...
-
IPv6 uses 128 bits for addressing. It is not easy to estimate/imagine how big this num- ber is. Here is one way how you can demonstrate this. Suppose each square millimetre on the Earth's surface is...
-
Which SDP component terminates network traffic and enforces communication policies? A . Client B . Access Manager C . Gateway D . Firewall E . Controller
-
The employer pays CPP premiums in what ratio to employee CPP deductions? O A. one-quarter of employee CPP deductions OB. 1.4 times employee CPP deductions OC. Matching employee CPP deductions D....
-
Sanchez Company uses a special payroll account to pay employees. The gross amount of the payroll this week is $5,320; the net amount is $4,545. Journalize the transfer of funds to the payroll account...
-
The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have...
-
Consider the suspension rod diameter measurements described in Exercise 8-27. Compute a 95% prediction interval on the diameter of the next rod tested. Compare the length of the prediction interval...
-
Consider the bottle wall thickness measurements described in Exercise 8-29. Compute a 90% prediction interval on the wall thickness of the next bottle tested.
-
How would you obtain a one-sided prediction bound on a future observation? Apply this procedure to obtain a 95% one-sided prediction bound on the wall thickness of the next bottle for the situation...
-
Differentiate between a scalar value and a vector value.
-
Now that the supplier of the nori has been chosen and the transportation method selected, you turn your attention to the downstream side of the supply chain -- the marketing (distribution) channels....
-
Mandy Murphy, owner of Murphy and Co. (Saint John, New Brunswick), gave the following list of assets and liabilities to a public accountant and asked him to prepare a balance sheet for the company as...
Study smarter with the SolutionInn App