Real Analysis/Advanced Calculus (Needs to be a full proof), Mathematics

Real Analysis/Advanced Calculus (Needs to be a full proof), Mathematics

Assignment Help:

Both need to be a full page, detailed proof. Not just a few lines of proof.

(1) “Every convergent sequence contains either an increasing, or a decreasing subsequence (or possibly both, of course).”
Proof: Suppose that lim(as n goes to infinity) x(sub n) = L. If infinitely many terms are equal to L, we are done. If not, either infinitely many terms are > L, or infinitely many terms are < L. Choose one option and complete the proof.

(2) Adapt carefully the bisection argument seen in the proof of Bolzano-Weierstrass to prove the Intermediate Value Theorem: If f is a continuous function on [a,b], and if f(a) and f(b) have opposite signs, then there exists a point c (a,b) such that f(c) = 0.
Proof: Suppose that f(a) < 0 and f(b) > 0. Denote a(sub 0) = a, b(sub 0) = b and consider the intervals [a, (a+b)/2] and [(a+b)/2, b].

Related Discussions:- Real Analysis/Advanced Calculus (Needs to be a full proof)

Phase plane, Before proceeding along with in fact solving systems of differ...

Before proceeding along with in fact solving systems of differential equations there's one topic which we require to take a look at. It is a topic that's not at all times taught in

Sas, can you tell me how to find the "x" and the "y" when trying to find if...

can you tell me how to find the "x" and the "y" when trying to find if two triangles are smiliar

Real numbers, prove root 2 as irrational number

prove root 2 as irrational number

Understanding quadrilaterals, how to find x,y and z in parallelograms,rhomb...

how to find x,y and z in parallelograms,rhombus etc.

What are real numbers, The hole set of irrational and rational numbers is t...

The hole set of irrational and rational numbers is the set of real numbers and is representing by R. Thus, the real numbers can also be describe in terms of position of a point on

Normal to y=f(x) , If the normal to y=f(x) makes an angle of pie/4 with y-a...

If the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is eqivalent to? Ans) The normal makes an angle 135 degree with the x axis. also f ''(1)

Determine the volume of the object, A rectangular container is 15 cm wide a...

A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the

Help, question..A Circular rug is 6 yards in diameter. Binding for the edge...

question..A Circular rug is 6 yards in diameter. Binding for the edge of the rug cost $2.00 per yard . what eill it cost to bind the rug

Percents, write as a percent 6/10

write as a percent 6/10

Estimate what percent of decrease for population, The population of Hamden ...

The population of Hamden was 350,000 in 1990. By 2000, the population had decreased to 329,000. What percent of decrease is this? First, ?nd out the number of residents who lef

Write Your Message!

Name

Email id

Message

Verfication Code

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!

Submit Assignment

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