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## Homework Statement

From the definition of the derivative, prove that, if f(x) is differentiable at x=c, then f(x) is continuous at x=c.

## Homework Equations

f'(c) = lim [f(x)-f(c)]/(x-c) This is the definition for a function to be differentiable at

x->c x=c.

## The Attempt at a Solution

we are required to prove that

lim f(x) = f(c) (this is what it means for the function to be continuous

x->c

lim f(x) - f(c) = 0

x->c

This looks alot like the numerator for the definition of differentiable at x=c.

From here, i'm lost.