Purchase Solution

Two-Sided Limits : g(x,y)=|x|y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b.

Not what you're looking for?

Ask Custom Question

G(x,y)=|x|y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b.

Purchase this Solution

Solution Summary

A two-sided limit proof is provided. The solution is detailed and well presented.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Problem 56471:

For a function f(x) to be differentiable at a point x = a, the following limit must exist and be finite:

. A limit written like this is a "two-sided" limit.

When one writes a limit as above, it means a "two-sided" limit. This means that if x approaches a from the left or the right, the limits must be the same, or the two-sided limit doesn't exist, so the limit doesn't exist. This can be found in most calculus books.

We write this as:
exists if and only if = <> +/-infinity.

So now we can say that a function ...

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.

Exponential Expressions

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

Solving quadratic inequalities

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

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.

Multiplying Complex Numbers

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