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More Limits - PowerPoint PPT Presentation

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. Do Now. Agenda. Do Now Review Limits – How to write them and evaluate them Graphically Limits Numerically

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More Limits

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

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

• 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

• “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.

• 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

• 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’

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

• Check the other side!

• 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.

• 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

• 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.

Page 87 #2

• Anton problem set

P. 76 #4 (quick check)

P. 87 (3-5, 9,10, 12, 29-32)