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### More Limits

Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically

Do Now

- For the graph of f pictured, evaluate the expressions below

Agenda

- Do Now
- Review Limits – How to write them and evaluate them Graphically
- Limits Numerically
- One Sided Limits
- Non-existent limits

Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically

Limits

- “The limit of f(x) as x approaches (or goes to) c”
- This means: What function value does the function approach as x gets closer and closer to c from both sides.

Agenda

- Do Now
- Review Limits – How to write them and evaluate them Graphically
- Limits Numerically
- One Sided Limits and Non-existent limits

Objective: SWBAT Evaluate one sided and two sided limits, and determine if a limit exists graphically

Evaluating Limits Numerically

- We can test to see what number a function is getting closer and closer to numerically.
- Calculators: put the following function in for Y1
- Go to Table Set, and change the independent variable(x) to ‘ask’ and the dependent variable to ‘auto’

Limits - Numerically

- Let’s find out what the limit of this function is as we approach x=4. Set up this table:

Similarly

- Check the other side!

Now you try

- As a table, I’ll give you a function, and an x value to approach.
- Sketch a graph of the function (including any holes or asymptotes)
- Create a table with values approaching from both sides.
- Evaluate the limit
- Put all of it on your spot on the board after checking with me.

Non-Existent Limits

- If a function does not converge (get closer and closer to one value) at a particular x value, we say it’s limit does not exist
- i.e.

Remember:One Sided Limits

- We can evaluate a limit from one direction.
- This is called a one sided limit

The limit of the function as x approaches c from the left

The limit of the function as x approaches c from the right

Numerically-the rules!!!

- If both sides of the table get closer to that value then it is that value
- If both sides of the table get larger and larger in the same direction then, the limit is positive or negative infinity
- If both sides of the table get larger in different directions, then the limit does not exist.

Eeeeek! What if I plug in and the universe explodes?

If you plug in you get 1/0 and the universe explodes.

In this case, you must solve numerically, or solve graphically.

Good news! It can be done in your head.

- For example, what happens to 1/x as you get closer and closer to 0, from the left. (x=-.1, -.01, -.001 etc).
- What about from the right? (x=.1, .01, .001 etc)
- This limit does not exist.

Together adding limits

Page 87 #2

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