Question

Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite...

Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite open interval and let u ∈ (a, b). Suppose that f : (a, b) −→ R is a function and that lim x−→u f(x) = L ∈ R. Prove that for every sequence an −→ u with an ∈ (a, b), we have t

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

i know your question is incomplete (last line is incomplete ) ...but i'm doing it..because this is well known question in real analysis...

please like and good rate ...

if you have any doubt you can ask in comment box before hit the dislike option ...because it's demotivate us..

thank you.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
. Write down a careful proof of the following. Theorem. Let (a, b) be a possibly...
. Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite open interval and let u ∈ (a, b). Suppose that f : (a, b) −→ R is a function and that for every sequence an −→ u with an ∈ (a, b), we have that lim f(an) = L ∈ R. Prove that lim x−→u f(x) = L.
Prove the following theorem: Theorem. Let a ∈ R and let f be a function defined...
Prove the following theorem: Theorem. Let a ∈ R and let f be a function defined on an interval centred at a. IF f is continuous at a and f(a) > 0 THEN f is strictly positive on some interval centred at a.
Write a careful proof that every group is the group of isomorphisms of a groupoid. In...
Write a careful proof that every group is the group of isomorphisms of a groupoid. In particular, every group is the group of automorphisms of some object in some category. Consider the `sets of numbers' listed in §1, and decide which are made into groups by conventional operations such as + and . Even if the answer is negative (for example, (K, ) is not a group), see if variations on the definition of these sets lead to groups (for...
Use Definition 4.2.1 to supply a proper proof for the following limit statements. (a) lim as...
Use Definition 4.2.1 to supply a proper proof for the following limit statements. (a) lim as x→2 of (3x + 4) = 10. (d) lim as x→3 of 1/x =1 /3. Definition 4.2.1 (Functional Limit). Let f : A → R, and let c be a limit point of the domain A. We say that limx→c f(x)=L provided that, for all ϵ>0, there exists a δ>0 such that whenever 0 < |x−c| <δ(and x ∈ A) it follows that |f(x)−L|...
1. Let D ⊂ C be an open set and let γ be a circle contained...
1. Let D ⊂ C be an open set and let γ be a circle contained in D. Suppose f is holomorphic on D except possibly at a point z0 inside γ. Prove that if f is bounded near z0, then f(z)dz = 0. γ 2. The function f(z) = e1/z has an essential singularity at z = 0. Verify the truth of Picard’s great theorem for f. In other words, show that for any w ∈ C (with possibly...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).
5. Let I be an open interval with a ∈ I and suppose that f is...
5. Let I be an open interval with a ∈ I and suppose that f is a function defined on I\{a} where the limit of f exists as x → a and L = limx→a f(x). Prove that the limit of |f| exists as x → a and |L| = limx→a |f(x)|. Is the converse true? Prove or furnish a counterexample.
Let f:[0,1]——>R be define by f(x)= x if x belong to rational number and 0 if...
Let f:[0,1]——>R be define by f(x)= x if x belong to rational number and 0 if x belong to irrational number and let g(x)=x (a) prove that for all partitions P of [0,1],we have U(f,P)=U(g,P).what does mean about U(f) and U(g)? (b)prove that U(g) greater than or equal 0.25 (c) prove that L(f)=0 (d) what does this tell us about the integrability of f ?
Let B be a (finite) basis for a vector space V. Suppose that v is a...
Let B be a (finite) basis for a vector space V. Suppose that v is a vector in V but not in B. Prove that, if we enlarge B by adding v to it, we get a set that cannot possibly be a basis for V. (We have not yet formally defined dimension, so don't use that idea in your proof.)
A. Let p and r be real numbers, with p < r. Using the axioms of...
A. Let p and r be real numbers, with p < r. Using the axioms of the real number system, prove there exists a real number q so that p < q < r. B. Let f: R→R be a polynomial function of even degree and let A={f(x)|x ∈R} be the range of f. Define f such that it has at least two terms. 1. Using the properties and definitions of the real number system, and in particular the definition...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT