# AP Calculus 2.5 Limits

AP Calculus 2.5 Limits. What is the limit?

AP Calculus | Limits |

MPAC 5 | Building notational fluency |

### Transcript

radiance Because of this the arc length is also x

A right triangle is created And the height of the

leg next to the ark of the circle is a

sign of acts Imagine what happens His ex gets smaller

and smaller Smaller It appears that the height of the

leg of the triangle and the are calling becomes indistinguishable

Or that as x approaches zero ex becomes sign of

acts Therefore the limit as x approaches zero signings over

x is equal Tio what And here the potential anthony

All right for this problem we should think of the

division in sine x over acts as the ratio between

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

able to get rid of that car waken See that

as angle x gets smaller and smaller the two legs

of the triangle get closer and closer in sign of

ex gets smaller and smaller waken See that arc link

with acts also gets smaller If x gets really small

we see that the ark in vertical get closer and

closer to each other until there nearly identical once Acts

become 0 They do become identical and the ratio between

the two is just one to one Therefore his ex

approaches Zero sign of ex overact approaches one on our

answer be