Question

Help me write out the proof of "If f(x) is differentiable at a, then f(x) is continuous at a."

Answer 1

compute

\[\lim_{x\to a}[f(x)-f(a)]\]

Answer 2

your move :)

Answer 3

It would be \[\lim_{x \rightarrow a} f(x)-f(a) \div x-a\]

Answer 4

plugging in a will give you 0/0

Answer 5

\[\lim_{x\to a}[f(x)-f(a)]=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}(x-a)=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}\lim_{x\to a}(x-a)=\cdots\]

Answer 6

I thought you can't directly multiply (x-a) to it since it will change the limit value.

Answer 7

I multiplied and divided by it...so i didn't change the value