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๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

1.12 Confirming Continuity over an Interval

#continuity

#interval

โฑ๏ธย ย 1 min read

written by

Jed Quiaoit

jed quiaoit


๐ŸŽฅWatch: AP Calculus AB/BC - Continuity, Part I

Simple polynomials are continuous everywhere; it's the trigonometric, rational, and piecewise functions that might have continuity problems.

The concept of continuity over an interval is quite simple; if the graph of the function doesnโ€™t have any breaks, holes, or other discontinuities within a certain interval, the function is continuous over that interval. However, this definition of continuity changes depending on your interval and whether the interval is closed or open.ย 

Confirming Continuity Over an Open Interval ๐Ÿ”“

Confirming continuity over an open interval is fairly easy:

"A function is continuous on the open interval if and only if the function is continuous at every point in the interval."

To put it simply, if you can trace the function from a to b without picking up your pencil, then the function is continuous over the interval. However, it is important to remember that this is an open interval. So, you actually start with your pencil at the point directly after a and ending at the point directly before b.ย โœ๏ธ

Confirming Continuity Over a Closed Interval ๐Ÿ”

Confirming continuity over a closed interval is a bit more complicated.ย 

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