Ace school

with brainly

  • Get help from millions of students
  • Learn from experts with step-by-step explanations
  • Level-up by helping others

A community for students.

I don't get the proof of Differentiable implies continuous. We prove that lim f(x) as x tends to x0 - f(x0) = 0 (which is the definition of continuous) by manipulating it to be f'(x) * 0. I don't see how this completes a proof. This just proves that f is continuous. In fact, in the accompanying notes it says that this shows "it’s true that lim f(x) (as x tends to x0) −f(x0) = 0, and it’s true that differentiable functions are continuous." I don't see where differentiable implies continuous in all of this. What am I missing?

OCW Scholar - Single Variable Calculus
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

I'm not sure what the question is. Starting from the assumption that f is differentiable at f(x0) and proving that it's continuous at f(x0) does prove that differentiability implies continuity. That's what implication means.
Haha yeah I thought about it some more and see it now. It was a long day when I asked the question. Continuous means that the (derivative of f(x)) - f(x0) = 0 and it's legimate to subtrace that f(x0) from any differentiable function. But doing that we see when end up the fact that it equals zero so we know any differentiable function is continuous at x0
*subtract

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question