Purchase Solution

Differentiable and continuous functions

Not what you're looking for?

Ask Custom Question

Suppose fâ?¶Râ?'R is twice differentiable with both f' and f'' continuous in an interval around 0. Suppose further that f(0)=0. Let
h(x)={f(x)/x, if xâ? 0,
f^' (0), if x=0.
Show that
(a) h is differentiable at x=0.
(b) h is differentiable at x=0 with h^' (0)=1/2 f^'' (0).
(c) h' is continuous at x=0.

Attachments
Purchase this Solution

Solution Summary

Differentiables and continuous functions are clearly exhibited.

Solution Preview

Proof:
Since is twice differentiable function, and are continuous in the neighborhood of 0, and , then we have
, where ...

Purchase this Solution


Free BrainMass Quizzes
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.

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.

Exponential Expressions

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