Honors Precalculus Notes--Chapter 11, Introduction to Calculus
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Course
Precalculus
Institution
Junior / 11th Grade
Chapter 11 notes for 11th grade Honors Precalculus from an A+ student. Includes definitions on course materials, graphs displaying concepts, numerous example problems including answers, equations, and step-by-step instructions designed to make learning a breeze! Chapter features 3 moduels, includi...
Finding Limits Using Graphs
The limit statement limflx ) =L
✗ → a
is illustrated in the figure .
In (a) , as In (b) , as ✗ In (c) , as x
✗
approchesa, approaches a
, approchesa , fcx )
flx ) approaches flx ) approches L .
approches L . Notice,
L Ata, the This true
.
is
although however, that the
value of the f is not defined at value of the function
function is a
,
shown by the ata, f(a) is not
L : f( a) =L hole in the graph .
equal to the limit .
, Example
Use the
graph to find each of the
following :
* asx
approches -2
Iim f( × ) =
5 yapproches 5
✗→ -2
^
* Not 5 because theres a hole .
t
fl 2) -
=
3 3 because it fills in the hole .
Example
if 3
{
✗ =/
2×-4
g( × , =3
=
Graph the function -
5 if ✗
Use the
graph to find lim flx )
✗ → 3
limflx ) = 2
^
✗→ 3
f. (3) = -5
V
One -
Sided Limits
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