Session 4: Limits and Continuity. What is a continuous function? One that continues through a point? But the function he drew with different left and right sides didn't continue through (0,1), it jumped up and continued at (0,2) It feels like the course assumes I know this, am I supposed to?

Question

phi · Answer

on the page http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-4-limits-and-continuity/ there are links to pdf "notes" that (try to) explain your question. The "intuitive" definition of continuous is that you can draw the curve *without* lifting your pen from the paper. Thus the example you cite **it jumped up*** is *not* continuous. The notes give the technical definition of continuous, which uses the definition of "left-handed" and "right-handed" limits

anonymous · Answer

Thanks for your help.

I went through all the notes again and I found some previous stuff I don't understand. In the notes to Clip 1: Limits, about two thirds down the first page, they start to explain left and right hand limits. I understand the plus means numbers greater than x0 but they seem to make x0=0 without explaining why. Can you help me understand this?

phi · Answer

You can find the limit of f(x) at any x, but there is only one "interesting point", where we have a jump. They want to know "what is going on" at the jump i.e. at x=0 Khan has lots of videos on calculus. Here is the one where he talks about continuity https://www.khanacademy.org/math/differential-calculus/limits_topic/continuity-limits/v/limits-to-define-continuity For more background on limits, try https://www.khanacademy.org/math/differential-calculus/limits_topic/epsilon_delta/v/limit-intuition-review and the videos in that section. There entire playlist for calculus is https://www.khanacademy.org/math/differential-calculus If you have questions on a particular topic, chances are there is a short video that talks about it.

anonymous · Answer

Thank you