Purchase Solution

Uniformly Continuous Functions and Mean Value Theorem

Not what you're looking for?

Ask Custom Question

Assume that f is differentiable for each x and there exists M>0
such that
for each x

Prove that f is uniformly continuous on D.

Hint: Can use the mean value theorem.

keywords: differentiability, continuity

Attachments
Purchase this Solution

Solution Summary

Uniformly Continuous Functions and the Mean Value Theorem are investigated. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

By assumption, there exists M∈R such that |f'(x)| for all x∈R. By the Mean Value Theorem, if x<y ∈ R ...

Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

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

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.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

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