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# 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