Chapter 2 - Definitions

Question 1

What is the definition for f to be differentiable (derivative) ?

Answer 1

Let f go from D to the real numbers, where D is some subset of the real numbers and a in D be a cluster point of D. Then f is differentiable at a if the limit ‘lim x to a of f(x)-f(a)/(x-a) exists.
The limit f’(a) is called the derivative of f at a.
f is differentiable if it is differentiable at a for all a in D.

Question 2

What is the definition for open?

Answer 2

U is a subset in the real numbers is open if for each a in U, there exists a delta greater than 0 such that (a-delta, a+delta) is a subset in U