# Calculus HW #1 differenciable

• November 15th 2006, 05:01 PM
Nimmy
Calculus HW #1 differenciable
1. Write the precise definition for a function f(x) defined for all values of x to be a differentiable function.
• November 15th 2006, 06:58 PM
ThePerfectHacker
Quote:

Originally Posted by Nimmy
1. Write the precise definition for a function f(x) defined for all values of x to be a differentiable function.

The derivative of a function $f$ is a function defined as, all the values in the domain such that,
$\lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$ exist (and at least one exists).
The map of the function is defined as its limit value.