Purchase Solution

Real Analysis : Neighborhoods

Not what you're looking for?

Ask Custom Question

Assume g:(a,b)->R is differentiable at some point c belong to (a,b). If g'(c)not= 0 show that there exists a delta neighborhood V_delta (c) subset or equal to (a,b) for which g(x) not= g(c) for all x belong to V_delta (c).

Purchase this Solution

Solution Summary

A neighborhood is investigated.

Solution Preview

Proof:

Since g'(c) is not 0, without loss of generality, we assume g'(c)>0. We know g'(c) is the limit of (g(x)-g(c))/(x-c) as x->c. When ...

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Graphs and Functions

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

Multiplying Complex Numbers

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

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.