Convergence, Mathematics

Assignment Help:

Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0.

(a) If (xn) converges to x, show that (|axn + b|) converges to |ax + b|.
(b) Give an instance , with brief justi cation, where (|xn|) converges but (xn) does not.
(c) If (|xn|) converges to 0, elustratethat (xn) converges to 0.

In (a) you need to use only the de nition of convergence and no other limit theorems.


Related Discussions:- Convergence

Find the sum of a+b and a-b, Find the sum of a+b, a-b, a-3b, ...... to 22 t...

Find the sum of a+b, a-b, a-3b, ...... to 22 terms. Ans:    a + b, a - b, a - 3b, up to 22 terms d= a - b - a - b = 2b S22 =22/2 [2(a+b)+21(-2b)] 11[2a + 2b - 42b] =

Decimals, what is 0.875 of 2282?

what is 0.875 of 2282?

Algorithm for division, ALGORITHM FOR DIVISION : If you ask a 10 or 1 1-ye...

ALGORITHM FOR DIVISION : If you ask a 10 or 1 1-year-old child to solve, say, 81 + 9, the chances are that she will correctly do it. But if you ask her to solve, say 72 + 3, t

Shares and dividend, A man buys rs50 shares of a company paying 12% of divi...

A man buys rs50 shares of a company paying 12% of dividendat premium ofof rs10 find market value of 320 shares and profit%

Chanllenge, apzza driver delivered 27 pizzas in one night he delivered more...

apzza driver delivered 27 pizzas in one night he delivered more then one pizza to only one house . every other hhouse he only delivered pizza to 18 houses . how many pizzas did he

Mathematical formulae, Mathematical Formulae (a ...

Mathematical Formulae (a + b) 2 = a 2 + b 2 + 2ab (a - b) 2 = a 2 + b 2 - 2ab (a + b) 2 +

Derivatives of inverse trig function, Derivatives of Inverse Trig Functions...

Derivatives of Inverse Trig Functions : Now, we will look at the derivatives of the inverse trig functions. To derive the derivatives of inverse trig functions we'll required t

Midpoint rule - approximating definite integrals, Midpoint Rule - Approxima...

Midpoint Rule - Approximating Definite Integrals This is the rule which should be somewhat well-known to you. We will divide the interval [a,b] into n subintervals of equal wid

Sums, what is 10 times 10 pls

what is 10 times 10 pls

Area with polar coordinates - parametric equations, Area with Polar Coordin...

Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves.  Note also that we said "enclosed by" in place of "under" as we usually have

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd