### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start remote presentation- Invited audience members
**will follow you**as you navigate and present - People invited to a presentation
**do not need a Prezi account** - This link expires
**10 minutes**after you close the presentation - A maximum of
**30 users**can follow your presentation - Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

### Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.

You can change this under Settings & Account at any time.

# Limits

Introduction to Limits, and how it relates to Rates of Change!

by

Tweet## Andrew Lanning

on 4 June 2010#### Transcript of Limits

Limits lim x - 1 = 2 - 1 = 1 x 2 What is 'x - 1' approaching

as x approaches 2?? The Graph: f(x) = x - 1 x y We just substitute x

into the equation! What about: lim x -3 (x + 3)(x + 2) ______________ (x + 3) Try substituting x = -3

into the equation... Let's Graph it! GeoGebra Where does the function not exist? What can we change the function to? What is the function approaching

as x approaches -3?? So... lim (x + 3)(x + 2) ______________ (x + 3) x -3 = lim (x + 2), x ≠ -3

= -3 + 2

= -1 x -3 What's happened?? The line is discontinuous at x = -3. Discontinuous Functions Look Like: A Gap Undefined point When have a:

divide by 0 (zero) Practice:

Ex 13B, page 634

Q: 1, 2, 4, 5, 6 (1st col)

Q: 10 (not c,f) AROC...............IROC................Motion Graphs...................Polynomials...........................First Principles................Rule.................. Rates of Change Learning Time Line A limit describes what a function

is approaching at a specific x value. Let's go outside!! 2 steps + 1 step + 1/2 step + ....

What do we approach?? If we walk towards a wall,

but only halfway of what's left

each time, what do we approach?? lim f(x) = f(a) x a "What is the function approaching as

x approaches a?" If continuous:

Just sub in x value If discontinuous:

Simplify, then sub in x.

Also, state x-value for

discontinuous. Helpful Tip: Practice:

Ex 13A, page 628

Q1, 2, 4, 8(abc),

9 (adgj), 12 http://www.123rf.com/photo_4568207.html

Full transcriptas x approaches 2?? The Graph: f(x) = x - 1 x y We just substitute x

into the equation! What about: lim x -3 (x + 3)(x + 2) ______________ (x + 3) Try substituting x = -3

into the equation... Let's Graph it! GeoGebra Where does the function not exist? What can we change the function to? What is the function approaching

as x approaches -3?? So... lim (x + 3)(x + 2) ______________ (x + 3) x -3 = lim (x + 2), x ≠ -3

= -3 + 2

= -1 x -3 What's happened?? The line is discontinuous at x = -3. Discontinuous Functions Look Like: A Gap Undefined point When have a:

divide by 0 (zero) Practice:

Ex 13B, page 634

Q: 1, 2, 4, 5, 6 (1st col)

Q: 10 (not c,f) AROC...............IROC................Motion Graphs...................Polynomials...........................First Principles................Rule.................. Rates of Change Learning Time Line A limit describes what a function

is approaching at a specific x value. Let's go outside!! 2 steps + 1 step + 1/2 step + ....

What do we approach?? If we walk towards a wall,

but only halfway of what's left

each time, what do we approach?? lim f(x) = f(a) x a "What is the function approaching as

x approaches a?" If continuous:

Just sub in x value If discontinuous:

Simplify, then sub in x.

Also, state x-value for

discontinuous. Helpful Tip: Practice:

Ex 13A, page 628

Q1, 2, 4, 8(abc),

9 (adgj), 12 http://www.123rf.com/photo_4568207.html