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Description:

AP Calculus: Problem Explanation Limits Drill 1, Problem 1. Which of the following are true about the pictured function?

Language:
English Language

Transcript

00:03

Here's an unshmoopy question you can write about tonight in your diary...

00:07

Which of the following are true about the pictured function?

00:10

I.   This function is not continuous at the point a.

00:13

II.  This function doesn't have a limit at point a.

00:17

III. This function isn't defined at point a.

00:21

Here are the potential answers...

00:25

OK, so we're given a graph and being tested on a few vocab words:

00:30

"Continuous"... "limit"... and "defined."

00:33

No short cuts here so we need to brute force and test each answer.

00:38

One... is the function continuous at point A?

00:41

Well, continuous means the function is defined at point A, and there's no hole in it.

00:47

From that hole and the actual point A, there's a pretty big jump...

00:50

...in other words, the function is NOT continuous at point A.

00:54

This is practically the textbook definition of DIScontinuous.

00:58

Ok check! One is true. So we can eliminate B, C, and E.

01:02

Movin' on.

01:03

Two... does the function have a limit at point A?

01:06

Well, to find the limit at point A, the right and left limits of point A must exist... that

01:12

is, they aren't divided by zero... and have the same values.

01:15

But if we look at the graph, the right and left limits of point A clearly have different values.

01:20

...here... and here...

01:21

The values are some positive y-value and a negative y-value, so... different.

01:27

The function does NOT have a limit at point A. 2 is true, so check!

01:32

We don't even have to check number 3 because there's no I, II, and III option. So D's our answer.

01:37

But for you overachievers, let's take a look at 3.

01:41

Is the function defined at point A?

01:43

Well, yes it is; there's a filled point at point A. So 3 isn't true.

01:48

So D is our answer...done.

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