Determining uniform convergence of functions

Reference no: EM13122507

1. Show that if a>0, then the convergence of the function nx/(1+n^2 x^2) is uniform on the interval [a,infinity), but is not uniform on the interval [0,infinity).

2. Show that if b is greater than 0 and less than 1, then the convergence of the function x^n/(1+x^n) is uniform on the interval [0,b] but is not uniform on the interval [0.1]. Note that x>0.

Reference no: EM13122507

Questions Cloud

Budgeted variable factory overhead rate : Davie Corporation is preparing its Manufacturing Overhead Budget for the fourth quarter of the year. The budgeted variable factory overhead rate is $6.00 per direct labor-hour; the budgeted fixed factory overhead is $92,000 per month, of which $16..

What is the probability none are a papers : A stack of 12 papers contains three "A" papers. If three papers are selected, what is the probability

If one ball is drawn at random : If one ball is drawn at random, find the probability it is red. If two balls are drawn, find the probability both are green. If two balls are drawn, find the probability one is red and the other is blue

Total costs of personnel : Dougherty Company employs 20 individuals. Eight employees are paid $12 per hour and the rest are salaried employees paid $3,000 a month. How would total costs of personnel be classified?

Determining uniform convergence of functions : Show that if a>0, then the convergence of the function nx/(1+n^2 x^2) is uniform on the interval [a,infinity), but is not uniform on the interval [0,infinity).

Find the probability that no two passengers get off : An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor

Work in process inventory : All of the following would be entries in assigning accumulated costs to the Work In Process Inventory except:

Concept of inverse variation-vertical asymptote : Explain the concept of inverse variation. Provide two examples. What is the vertical asymptote for the function y = ( x^2 - 4) / ( x - 2 )?

Raw materials inventory problem : As of December 31, 2010, Stand Still Industries had $2,500 of raw materials inventory. At the beginning of 2010, there was $2,000 of materials on hand. During the year, the company purchased $305,000 of materials;

User Account

All Pages