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# Limits

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

## Andrew Lanning

on 4 June 2010

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#### 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