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

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More limits

More Limits

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


Do now
Do Now

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



Agenda
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
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.


Agenda1
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
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
Limits - Numerically

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


Similarly
Similarly

  • Check the other side!


Now you try
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
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
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
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
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.




Homework
Homework

  • Anton problem set

    P. 76 #4 (quick check)

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


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