a) Prove that x/n 0 uniformly, as n , on any closed interval [a, b]

Question:

a) Prove that x/n → 0 uniformly, as n → ∞, on any closed interval [a, b]
b) Prove that 1/(nx) → 0 pointwise but not uniformly on (0, 1) as n → ∞.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:08 AM

See More Questions

Let V be an inner product space. (a) Prove that (x. v) = 0 for all v V if and only if x = 0. (b) Prove that (x. v) = (y. v) for all v e V if and only if x = y. (c) Let v1,...,vn be a basis for V....
a) Prove that (x")' = nxn-1 for every n eN and every x e R. b) Prove that (xn")' = nxn-1 for every n -NU{0} and every x (0, ).
Let H V Rn, with H convex and V open, and suppose that : V Rn is C1. a) Show that if E is a closed subset of H and then h(x)/||h|| 0 uniformly on E, as h 0. b) Show that if R is a closed...
Why is globalization of industries a common factor today?
The Short-Line Railroad is considering a $140,000 investment in either of two companies. The cash flows are as follows: a. Using the payback method, what will the decision be? b. Explain why the...
How do the managers of a business maintain its competitive position.
Consider the fuel consumption data in Table B.18. Regressor $x_{1}$ is an indicator variable. Perform a thorough analysis of these data. What conclusions do you draw from this analysis? y X2 X3 X4...
The Pew Research Center has conducted extensive research on the young adult population (Pew research website, November 6, 2012). One finding was that 93% of adults aged 18 to 29 use the Internet....
Tracy is single and had adjusted gross income of $35,800 in 2018. Tracy also has the following items: How much may Tracy claim as itemized deductions?
Demand for a certain product is 25,000 units/yr. Unit cost is $10.00. Holding cost rate is 30%/yr. Changeover (setup) time between products is 10.0 hr, and downtime cost during changeover is $150/hr....
Suppose that [ak] is a sequence of nonzero real numbers and that exists as an extended real number. Prove that k=1 ak converges absolutely when p > 1. ak+1 (1- p= lim k (1- ak
Let E be a nonempty subset of R and f be a real-valued function defined on E. Suppose that fn is a sequence of bounded functions on E which converges to f uniformly on E. Prove that uniformly on E as...
Does GAAP specify the minimum amount that a company must pay into its pension fund each year? If not, how is the amount determined?
The costs of putting goods into a saleable condition should be charged to (A) The trading account (B) The profit and loss account (C) The statement of financial position (D) None of these
When depositing money in your current account you should always use (A) A cheque book (B) A paying-in slip (C) A cash book (D) A general ledger
Net profit is calculated in the (A) Trading account (B) Profit and loss account (C) Trial balance (D) Statement of financial position
Which of these best describes non-current assets? (A) Items bought to be used in the business (B) Items which will not wear out quickly (C) Expensive items bought for the business (D) Items having a...
The descending order in which current assets should be shown in the statement of financial position is (A) Inventory, Accounts receivable. Bank, Cash (B) Cash, Bank, Accounts receivable, Inventory...
A plane wave in a lossless medium ( = 0, = 2 o , = 8 o ) is given as E = 60sin(t 10z)a x + 30sin(t 10z + /6)a y V/m. This wave is incident on a lossless medium ( = 0, = o , = 16 o )....
The area of a rectangle is 30 cm 2 and its perimeter is 26 cm. Find the length and width of the rectangle.
The life in hours of a 75-watt light bulb is known to be normally distributed with = 25 hours. A random sample of 20 bulbs has a mean life of X = 1014 hours. (a) Construct a 95% two-sided confidence...
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with 2 = 1000(psi)2. A random sample of 12 specimens has a mean compressive strength...
Suppose that in Exercise 8-12 we wanted to be 95% confident that the error in estimating the mean life is less than five hours. What sample size should be used?
b. Using the inference rules show that S can be inferred if the following logical sentences are believed. 1. P 2. ZvH 3. Hv-P 5. H K 6. K (Sv-P) 7. (Z^-H)K 4. Sv(K) 8. (KA-Q) S Give your answer in...
1) Write a "C" program, which finds only a path (not all the paths) between two given cities according to the directed graph below. This program also calculates the distance between given these two...
How does MariaDB leverage optimizer enhancements such as Cost-Based Optimization (CBO), Index Condition Pushdown (ICP), and Histogram-Based Statistics to improve query execution efficiency and plan...

a) Prove that x/n 0 uniformly, as n , on any closed interval [a, b]

Question:

Step by Step Answer:

a Given 0 choose N so large that N maxa b Then n N and x a b impl...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions