More Limits

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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

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.