This document outlines a lesson plan on limits and operations on limits: - Students will complete a worksheet on properties of limits and be introduced to basic operations on limits through examples. - The class will examine limits of functions using direct substitution and properties/operations on limits. - An activity asks students to find limits of monomial functions using only direct substitution. - The lesson includes a group work portion to discuss worksheet problems and a presentation on visualizing limits.

1. May 26, 2015
Aim: How do we solve problems involving the
Properties of Limits? How do we use the Operations
on Limits to solve problems?
Homework 69: Finish Worksheet probs on Properties of
LIMITS. Pg 875/ 47-48; pg 874/ 17-21 [in that order]. In
addition (if time permits), pg 884/ 13-16.
CCSS A-REI 11: Reasoning w/ Eqns (Limits)
DO NOW: Determine the following:

2. May 26, 2015
Do Now Problem(s) 5-7 min
Motivation 2-3 min
Development 10-15 min
Group Work Activities 15-18 min
Wrap-up, Summary 5 min
(Exit Slips)
Lesson Agenda:
Lesson Duration: 45 min

3. May 26, 2015
We can define general Properties of
LIMITS. And we can also define basic
mathematical Operations on Limits?
Do you think that these "general" Properties and
Operations would be useful? Why? Can you predict
what types of problems could be solved if basic
operations on Limits were proven to be mathematically
correct?
General Limit PROPERTIES and OPERATIONS allows
us to apply the idea of limits to many different problems
and also to prepare the foundation for integral and
differential calculus.

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Some Properties of LIMITS

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And the basic Operations on LIMITS

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11. May 26, 2015
Suppose
we
have
2
functions:
f(x)
=
x2
+
1
and
g(x)
=
x
–
4
Let's
compare
the
resulting
limits
of
functions
(involving
f(x)
and
g(x))
obtained
by
Direct
Substitution
(only)
AND
then
by
using
the
Properties
and
Operations
on
Limits.
Some Examples

12. May 26, 2015
Let's
examine
some
limits
involving
f(x)
and
g(x).
[Note:
f(x)
=
x2
+
1
and
g(x)
=
x
–
4]
Using
Direct
Substitution,
let’s
find
the
limits
of
the
functions
below.
Some Examples

13. May 26, 2015
Let's
examine
other
limits
involving
f(x)
and
g(x).
[Note:
f(x)
=
x2
+
1
and
g(x)
=
x
–
4]
And
now
let's
use
the
Properties
and
Operations
on
Limits
to
find
these
limits.
Some Examples

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A
Quick
Medial
Assessment:
(Pair-­‐Share)
For
this
activity,
"Direct
substitution
ONLY
ALLOWED
for
monomials"
[2.5
Minutes]
Find
the
function
limits
shown
below:
Students
with
an
odd
OSIS
#,
do
the
problem
in
RED
and
those
with
an
even
OSIS
#,
do
the
problem
in
BLUE.

16. May 26, 2015
Limits: PPT Presentations,
Simulations (Visualization)
KEY-PRECALCULUS-DOCS 12-1IntroLimits.docx
https://www.desmos.com/calculator/qxwfuihzzz
_____1.2 calculus powerpoint.pptAPCN13.2.ppt

17. May 26, 2015
Group Work:
Students are to get into your assigned groups and
discuss the worksheet problems 1-4 and 9-12.
After a predetermined time, selected group
members will report back to the class.
Summary
Exit Slips

18. May 26, 2015