F differentiable proves continuity

[mike1967]

Homework Statement

If f is differentiable at x then f is continues at x

Any help would be great.

Homework Equations

MUST USE epsilon delta definition to prove

The Attempt at a Solution

 

[mike1967]

I can prove like this:

(sorry I don't know how to make look fancy)



lim f(a+h) - f(a)/h = f'(a)
h->0

lim [f(a+h) - f(a)/h]*h = f'(a)*(h=0)
h->0

lim f(a+h) - f(a) = 0
h->0

lim [f(a+h) - f(a)]+f(a) = 0+f(a)
h->0

x= a+h h=x-ah

lim f(x) = f(a)
x->a