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:

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

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.

May 26, 2015

Some Properties of LIMITS

May 26, 2015

May 26, 2015

And the basic Operations on LIMITS

May 26, 2015

May 26, 2015

May 26, 2015

May 26, 2015

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

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

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

May 26, 2015

May 26, 2015

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.

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

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

May 26, 2015