Warm-up Enter the two functions into the y = in your 5 Enter the two functions into the y = in your graphing calculator    

Warm up Warm up 1. 2. 3. 4. 5. 6. Do in notebook Decide whether the problem can be solve with or without calculus. Explain your reasoning. 1. 2. 3. 4. Warm up 1. 2. 3. 4. 5. 6. Do in notebook

Be seated before the bell rings DESK Agenda : warm-up Go over homework homework quiz Notes lesson 1.2 Warm-up (in your notes) homework

Notebook 2) 1-2 Finding limits graphically and numerically Learning Target 1 Table of content Page 1-1 A Preview of Calculus 1 2) 1-2 Finding limits graphically and numerically Section HW Assignment Completed? Quiz Score 1.1  p.47: 4-6, 9   1.2 p. 55 1-27 odd, 57-60 all, 66-70 all

1-2 Finding limits graphically and numerically Example 1 : Limit : What does the function do as we approaches a value   What’s the y-value as x approaches 1? 1 X 1 Y Read: “ The limit as x approaches 1 is 3”

In general : The limit as x approaches c is L   The limit as x approaches c is L The limit as x approaches from the right of c is L The limit as x approaches from the left of c is L

Example 2 :   X 0.75 0.9 0.99 0.999 1 1.001 1.01 1.1 1.25 Y The limit does not exist (DNE) because the left hand limit does not equal the right hand limit Graphically Confirm :

  Example 3 : X 1.75 1.9 1.99 1.999 2 2.001 2.01 2.1 2.25 Y The limit does not exist (DNE) because of the unbounded behavior Graphically Confirm :

Example 3 : X Y The limit does not exist (DNE) because of the Oscillating Behavior Graphically Confirm :

Some graphs to think about ??? Does the limit exist. If not explain.  

Some graphs to think about ??? Does the limit exist. If not explain.

Left and right hand limits

Summary The limit exist when….. 3 ways a limit may fails to exist at x = c when…..

Summary