ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

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

1.13 Removing Discontinuities

#discontinuities

โฑ๏ธย ย 1 min read

written by

Anusha Tekumulla

anusha tekumulla


๐ŸŽฅWatch: Calculus AB/BC - Continuity, Part II

This topic focuses on how we can remove discontinuities from a function. If the limit of a function exists at a discontinuity in its graph, then it is possible to remove the discontinuity at that point so it equals the lim x -> a [f(x)].

We use two methods to remove discontinuities in AP Calculus: factoring and rationalization.ย 

Removing Discontinuities Using Factoringย 

If you are able to factor the function, you might be able to cancel out the part of the function that is causing the discontinuity.ย Thus, youโ€™ll be able to find the limit without having problems with discontinuities. To understand this, letโ€™s look at an example.ย ๐Ÿ™…โ€โ™‚๏ธ๐Ÿ™…

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(424).png?alt=media&token=b0eb5029-1fc2-42fd-8b5f-28f951eb8e92

Removing Discontinuities Using Rationalization

Another way to remove discontinuities is to rationalize the fraction. To do this we multiply by a complex conjugate. To understand this better, letโ€™s look at an example.ย ๐Ÿง 

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(426).png?alt=media&token=d02d1b08-1b6a-47ab-b1c7-524aec292c46

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