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

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

Find the time it takes to slide down, The time in seconds that it takes for...

The time in seconds that it takes for a sled to slide down a hillside inclined at and angle θ is where d is the length of the slope in metres. Find the time it takes to sli

What is venn diagram, The diagrams drawn to given sets are called as Venn d...

The diagrams drawn to given sets are called as Venn diagrams or Eule -Venn diagrams. Here given the universal set U by points within rectangle and the subset A of the set U given b

Mensuration, A palm tree of heights 25m is broken by storm in such a way th...

A palm tree of heights 25m is broken by storm in such a way that its top touches the ground at a distance of 5m from its root,but is not separated from the tree.Find the height at

Alcohol Solutions, If you have 60% alcohol and wish to dilute with water to...

If you have 60% alcohol and wish to dilute with water to make 12 liters 40% alcohol, How many liters of water should you add?

Vectors, why minimum three coplanar vectors are required to give zero resul...

why minimum three coplanar vectors are required to give zero resultant and not two?

Explain prime numbers vs. composite numbers, Normal 0 false f...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Equation of a straight line, In a two dimensional case, the form of t...

In a two dimensional case, the form of the linear function can be obtained if we know the co-ordinates of two points on the straight line. Suppose  x' and  x"  are two

Calculus, f(x)= 2e^5x+6 find the domain of f and find x-intercept.

f(x)= 2e^5x+6 find the domain of f and find x-intercept.

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