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AP Calculus Videos 13 videos

AP Calculus AB/BC 1.5 Limits
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AP Calculus: AB/BC Limits Drill 1, Problem 5. Evaluate the limit.

Limits at Infinity
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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
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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....

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AP Calculus 2.5 Limits 201 Views


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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

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