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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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