Purchase Solution

Proof that uses limiting values of functions

Not what you're looking for?

Ask Custom Question

Propose a definition for limit superior lim sup_x-->x_0;x belonging to E of f(x) and limit inferior lim inf_x-->x_0; x belonging to E of f(x) and then propose an analogue of the following for your definition and prove that analogue

Let X be a subet of R, let f: X-->R be a function, let E be a subset of X, let x_0 be an adherent point of E, and let L be a real number. Then the following two statements are logically equivalent:

1) f converges to L at x_0 in E
2) For every sequence (a_n) of n=0 to infinity which consists entirely of elements of E, which convergest to x_0, the sequence (f(a_n)) from n=0 to infinity converges to L.

Purchase this Solution
Solution Summary

The expert examines proofs that uses limiting values of functions.

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Integral Identity Question Involving Sin Functions

    A proof I'm trying to understand uses the following step, which I can't quite follow: Say . This implies that if , then , which further implies that: I understand the first inequality in the above line, but I don't see why .

  • Bessel functions

    This problem tells us that Bessel functions of half-integer order can be expressed in terms of polynomials and the sin and cos functions.

  • Functions: Proof by Induction

    The proof needs to look at the values of n, not x" This is the second time I have posted this problem, the first time someone tried to prove it by looking at the values of x, not n.

  • Moment Generating Functions

    Use moment generating functions to find the limiting distribution of .

  • Differentiable Functions : Lipschitz and Absolute Values

    Proof: I claim that (a) can imply (b).

  • Can lim x->0+ f '(x) and lim x->0- f '(x) exist and differ?

    The solution is a step by step proof of that fact comprising 3/4 of a page in Word with equations written in Mathtype.

  • Measurable function

    89896 Measurable Functions Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x. Please make sure to show the proof in both directions.

  • Set of functions with a continuous derivative

    48761 Set of functions defined on [0,1] that have a continuous derivative there ( one-sided derivatives at the endpoints). A).

  • NOR and NAND Connectives Proof

    The professor explained it but I still don't get it, it seems that the key of the proof rely on the EVEN/ODDNESS of the occcurrence at which the truth function takes the FALSE and TRUE values on the truth table. (no idea why...)

View More Related Solutions