# Real Analysis : Sequences and Limits

Not what you're looking for?

Show that if f be a function defined on A, and c be a limit point of A. If there exist two sequences (x_n) and (y_n) in A with x_n not =c y_n not = c and lim x_n=limy_n=c but lim f(x_n) not = f(y_n), then we conclude that the functional limit

lim_x-->c f(x) does not exist.

##### Purchase this Solution

##### Solution Summary

A proof involving sequences and limits is provided. The solution is concise.

##### Solution Preview

Proof:

If the limit of f(x) as x->c exists, suppose the limit is L, then for any e>0, there is a d>0, such that when |x-c|<d, we have ...

##### 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.

##### Graphs and Functions

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

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### 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.