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Calculus 1: Continuity and the Intermediate Value Theorem (Video #5) | Math with Professor V

Math with Professor V

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In this video, we explore continuity and the Intermediate Value Theorem (IVT). You’ll learn how to determine whether a function is continuous, the types of discontinuities that can occur, and how to apply the IVT to prove the existence of solutions.

This lesson also covers AP Calculus Unit 1: Limits & Continuity (AB/BC).
It’s perfect for AP Calculus exam prep, review, and practice problems — especially for students learning how to justify continuity and apply the IVT in AP-style questions. Add this video to your AP Calculus Unit 1 review playlist for complete coverage.

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14 Comments

@nyx0101 1 year ago

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@PaulManzini-y6v 2 years ago

Thank you for your service 🙏

@sajadsakhizada8005 1 year ago

God bless you. I love your content. I wish you the best.

@hhele1063 3 months ago

Thank you for your videos! I have a question here. In the example where two "c's" can exist, the N chosen is not between F(a) and F(b).....Does this still work?

@nethmijayasinghe3380 7 months ago

You deserve many more subscribers^^^

@robertmartian 8 months ago

grateful for you and your vids! you rad

@georgesadler7830 5 years ago

Professor V, thank for another excellent lecture on Continuity and the Intermediate Value Theorem from Calculus One. The examples and illustrations are amazing. I am really learning from these lectures.

@euphoria4502 4 months ago

Thank you for your videos. I never thought I was a math person but I’m really trying to be. Thank you professor V 🩷

@noaifekoya 1 year ago

You're the best. Thank you 🙏

@sajadsakhizada8005 1 year ago

Thanks for organizing all of your playlists. keep it up.

@ScottPalmer-mp1we 2 months ago (edited)

Thanks for the fine video. I must be missing something here but I don't understand how f(1) is defined. Wouldn't that make the function indeterminate? Ok, I get it, it's from factoring and canceling because subbing in 1 gives a real number answer.

@xhander7970 1 year ago

thank youuu for reals you are helping me survive my calc 1

@PaulManzini-y6v 2 years ago

Prof I wanted to ask a question.
Is Intermediate value property same as Intermediate value theorem
Coz theres a Q that wants the Intermediate value property and when I try looking it up on YouTube IVT appears