ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


AP Calculus AB Videos 14 videos

Derivatives as Slope of a Curve
5239 Views

What do snickerdoodles and velocity have in common? Derivatives! No, that wasn't a bad attempt at a joke. Get on our level by watching this speedy...

AP Calculus 1.3 Derivatives
224 Views

AP Calculus 1.3 Derivatives. Compute the limit.

Introduction to Integrals with Riemann Sums
620 Views

Riemann sums are a way to estimate the area under a curve. Check out the video for all the deets.

See All

AP Calculus 2.5 Limits 201 Views


Share It!


Description:

AP Calculus 2.5 Limits. What is the limit?


Transcript

00:00

Thank you We sneak and here's your shmoop du jour

00:05

brought to you by diagrams not the preferred method of

00:09

birth control All right consider the following diagram The picture

00:13

is of a wedge of a circle with a radius

00:15

of one The angle is acts which is measured in

00:18

radiance Because of this the arc length is also x

00:23

A right triangle is created And the height of the

00:25

leg next to the ark of the circle is a

00:27

sign of acts Imagine what happens His ex gets smaller

00:31

and smaller Smaller It appears that the height of the

00:36

leg of the triangle and the are calling becomes indistinguishable

00:39

Or that as x approaches zero ex becomes sign of

00:44

acts Therefore the limit as x approaches zero signings over

00:48

x is equal Tio what And here the potential anthony

00:54

All right for this problem we should think of the

00:55

division in sine x over acts as the ratio between

00:59

sign of x and x don't worry reason we'll be

01:02

able to get rid of that car waken See that

01:05

as angle x gets smaller and smaller the two legs

01:09

of the triangle get closer and closer in sign of

01:11

ex gets smaller and smaller waken See that arc link

01:14

with acts also gets smaller If x gets really small

01:18

we see that the ark in vertical get closer and

01:20

closer to each other until there nearly identical once Acts

01:24

become 0 They do become identical and the ratio between

01:28

the two is just one to one Therefore his ex

01:30

approaches Zero sign of ex overact approaches one on our

01:34

answer be

Related Videos

AP Calculus AB/BC 1.1 Limits
521 Views

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

AP Calculus AB/BC 1.5 Limits
265 Views

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

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?