Is f(x) continuous at x=3? | Definition of Continuity

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High School Math Teacher explains whether f(x) is continuous at x=3 using the definition of continuity.

The 3 Steps to the Definition of Continuity are:
1) f(c) exists
2) the limit as x approaches c exists
3) f(c) = the limit as x approaches c of f(x)

If these 3 steps are true, then f(x) is continuous at x=c.

Please leave a comment about any questions or thoughts you have!

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You seriously helped me in my Calculus today. I was lost on how to do this with the book explanation, but you explained it perfectly.

funkmonster

I love the organized structure you used in this video - you stuck to the definition of continuity step by step which was very easy to follow, and it was super helpful to have the definition off to the right and the specific case in this example off to the left! You made it very clear what notation to model which is often something students neglect, so this video will have a lot of value for students still getting used to proper upper level mathematical notation. The flow and explanations of this video were quite ...CONTINUOUS - there no were no holes (or Vertical Asymptotes!) in your explanations whatsoever!! 😁 Thanks for another awesome weekly video - fantastic work!

camwizemusic

This topic has been overlooked for quite some time until the advent of machine learning and artificial intelligence. Thanks for presenting a simplified strategy in answering a problem like this! Cheers, Christee. 😍🤓🥰

trewaldo

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