Download Limits - Ms. Huls` Math Class

Welcome to The Introduction to
CALCULUS!
By the way, this is our last topic!
1. Take out your HW #1 and HW #2
2. Do Warm-Up on Whiteboard!!!
o HW #3: p 903 #7- 33 (every other odd), p 909 #13-41
every other odd, #53
Agenda
1. Go over HW
2. Limits Algebraically
1. Limt MATHO
2. Closure
Learning Objective #1
By the end of this period you will be able to:
① Calculate limits of polynomial and rational functions
algebraically
Review HW
1. Piece-wise
2. Limit Worksheet
Limits
Take out your composition notebook and title it:
Limits- Algebraically
Limit Worksheet
o Work on the worksheet
15.1: Limits
Limit of a Continuous Function
o f(x) is continuous at a if and only if
o Examples: polynomials, sinx, cosx, and ax , and
15.1: Limits
Table- Talk:
o In Example 1(b) where is the graph continuous? Where
is it discontinuous?
Example 2
Whiteboards!
Whiteboards!
Evaluate:
This is not continuous at x=1 because it becomes 0/0.
15.1: Limits
Limit of a Discontinuous
Function
o When it is not continuous (
when you get 0/0) you
need to try to decompose
the function into simpler
ones by factoring.
15.1: Limits
When computing the limit, we are
only interested in x-values close to
1. What happens when x=1 is
irrelevant, so we can replace f(x)
with the simpler expression (x+1).
Therefore, the limit is 2 because it
gets closer and closer to 2.
15.1: Limits
Figure out the Limit…
https://www.youtube.com/watch/?v=oDAKKuBtDo
Whiteboards!
Limit MATHO
On your card, write down the following answers
ANYWHERE!









•
-1/9
2
6
4
9/2
6
-4
11
11/2
-3
• DNE ( not
defined from
left)
• 3/5
• 2
• -3
• -1
• -5
• ½
• DNE
•
•
•
•
•
4/3
-8
21
9
-11
Limit MATHO
1. I am going to pull a question out of the bin and you
are going to answer it in your composition
notebook.
2. If you get the answer, cross it out on your MATHO
sheet
3. First person to get 5 in a row across, down, or
diagonal WINS! I will give you piece of chocolate!
4. Questions?
Closure
Answer the following questions in your groups:
① What is a limit?
② How do you know if a limit is continuous or
discontinuous?
③ If a limit is discontinuous what do you need to do to
solve it algebraically?
Limit Chalk!
The weather is SO NICE so let’s go outside!!
Period 3 already drew beautiful graphs for us with limit
questions. You and your table group are going to go
outside and answer the questions.
Each student needs to be working!
Questions?