Thread: Limit Continuity

check continuity at point


Hello MHF, please help me with this exercise.

A function is continuous at a point x if
1) It is defined at that point.
2) The function approaches the same value as you approach x from the left as it does when you approach x from the right.
3) The function value is equal to this limiting value.

The question's a little weird - I think you're probably supposed to take the limit of all three expressions as x goes to 0. Give each one a try and let us know how far you get. You'll probably need l'Hôpital's rule at a minimum.

It probably doesn't help much, but for the second expression, you can take the limit as x goes to zero taking on only negative values, and for the third expression, you can take the limit as x goes to zero taking on only positive values.

The first expression shouldn't have a limit - that's why I said the question was weird.

- Hollywood

I'm also thinking strange because the f(0) doesn't exist...