ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


AP Calculus Videos 13 videos

AP Calculus AB/BC 1.5 Limits
265 Views

AP Calculus: AB/BC Limits Drill 1, Problem 5. Evaluate the limit.

Limits at Infinity
654 Views

If you're working on developing a positive self-image, don't ever weigh yourself on planet Deneb-G73. Either the gravitational pull there is a tad...

Graphing and Visualizing Limits
1041 Views

Breathe in deeply through the nose... Now slowly exhale... Breathe in... And out... Now visualize the graph of the limit of f(x) as x approaches 2....

See All

AP Calculus AB/BC 1.1 Limits 521 Views


Share It!


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.

Related Videos

AP Calculus AB/BC 1.5 Limits
265 Views

AP Calculus: AB/BC Limits Drill 1, Problem 5. Evaluate the limit.

Limits at Infinity
654 Views

If you're working on developing a positive self-image, don't ever weigh yourself on planet Deneb-G73. Either the gravitational pull there is a tad...

Graphing and Visualizing Limits
1041 Views

Breathe in deeply through the nose... Now slowly exhale... Breathe in... And out... Now visualize the graph of the limit of f(x) as x approaches 2....

AP Calculus 1.4 Limits
231 Views

AP Calculus 1.4 Limits. Given the limit, which of the following are true?

AP Calculus 2.3 Limits
208 Views

AP Calculus 2.3 Limits. Which of the following facts is helpful in determining the limit?