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

Experiments probabillity of compound events, what is the expiremental proba...

what is the expiremental probability that the next toss and spin will result in 3 and tail if 1-heads,53.2-heads,49.3-heads,54.1-tail,65.2-tails,71.3-tails,62

Triangles, ABCD is a parallelogram which AB and CD are divides by P and Q. ...

ABCD is a parallelogram which AB and CD are divides by P and Q. Such that AP:PB=3:2 and CQ:QD=4:1. If PQ and AC are meet at R, show that AR=3/7AC.

Marketing., what is product life cycle

what is product life cycle

Divides a given line segment internally in the ratio of 1:3, Divides a give...

Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let

Mean value theorem find out all the numbers c, Find out all the numbers c t...

Find out all the numbers c that satisfy the conclusions of the Mean Value Theorem for the given function.                                               f ( x ) = x 3 + 2 x 2 -

The mean value theorem with proof, The Mean Value Theorem  Assume f(x)...

The Mean Value Theorem  Assume f(x) is a function that satisfies both of the subsequent. 1.   f(x) is continuous on the closed interval [a,b]. 2.   f(x) is differentiabl

Mean and standard deviation, Q. Mean and Standard Deviation? Ans. ...

Q. Mean and Standard Deviation? Ans. The normal distribution is totally described if we know the average and standard deviation. - the population mean of the distribu

Terminology related to division, Terminology related to division :   A goo...

Terminology related to division :   A good way to remedy this situation is to familiarise children with these concepts in concrete, contexts, to start with. For instance, if a chi

1, what''s the beneit of study mathematics ?

what''s the beneit of study mathematics ?

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