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