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

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Find the maxima or minima and green theorem, 1) find the maxima and minima ...

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

Math, 1+3+5+7+9+11+13+15+17+19

1+3+5+7+9+11+13+15+17+19

What was the total cost of the copies, Mary made 34 copies at the local off...

Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0

Project, transportation problem project

transportation problem project

How to converting fractions to decimals explain with example, How to Conver...

How to Converting Fractions to Decimals explain with example? To convert fractions to decimals, divide the numerator by the denominator. The quotient is the decimal. Ex

Operation research, Advantages and disadvantages of operation researchs

Advantages and disadvantages of operation researchs

Theorem of continuous functions, Consider the subsequent IVP. y' = f(t,y...

Consider the subsequent IVP. y' = f(t,y) ,        y(t 0 ) = y 0 If f(t,y) and ∂f/∂y are continuous functions in several rectangle a o - h o + h which is included in a

Hypothesis testing of the difference between proportions, Hypothesis Testin...

Hypothesis Testing Of The Difference Between Proportions Illustration Ken industrial producer have manufacture a perfume termed as "fianchetto." In order to test its popul

Exponets, what does the three mean in the power ?

what does the three mean in the power ?

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