Limits - Day 1 Graphical Method PDF

Finding limits using GRAPH DAY 1 NEW TOPIC  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer func...

Finding limits using GRAPH DAY 1 NEW TOPIC  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer function REVIE  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer function REVIE  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer function REVIE  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer function REVIE  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer function REVIE  What function is shown by the graph on the left?  Piecewise function  Quadratic function  Linear function  Absolute value function  Greatest integer function REVIE  (1,4 ) REVIE  (1,4) (0,1) {(-2,-5),(-1,-2),(0,1),(1,4)… (x, f(x)} (-1,-2) (-2,-5) REVIEW LIMITS in real life… What is the maximum speed of a vehicle entering a school zone? A.) 20 kph b.) 25 kph b.) 30 kph MOTIVATION  What is the maximum LIMITS in real life… capacity of the water jug like this? A.) 4 galloons b.) 5 galloons b.) 6 galloons MOTIVATION LIMITS in real life… What is the credit limit of BDO credit card? A.) 60,000 b.) 70,000 b.) 100,000 MOTIVATION  1.) As a spectator, is it possible to get inside the ring during the fight? 2.) How closer can you get in order to get a better picture of what’s happening in the ring? 3.) From the closest distance to the ring, can you already get a picture of MOTIVATION what’s happening   Illustrate the limit of a function using the graph. STEM_BC11LC-IIIa-1 OBJECTIVE  Closer and closer BUT not really there ! 7  Using the given graphs, in your activity sheets, draw a vertical line from the x-axis to the graph.  Then, draw a horizontal line from the graph to the y-axis.  Do this repeatedly for 3 values to the left and right of the given x-value.  Do the tasks in 10 minutes.  Follow the first example. 2 ACTIVITY  DEMO EXAMPLE 7 2 ACTIVITY TASK 1 Q: What have you noticed here? 2 ANALYSI 1 TASK 2 Q: What have you noticed here? 2 ANALYSI 2 TASK 3 Q: What have you noticed here? 3 1 TASK 3 ANALYSI TASK 4 Q: What have you noticed here? 5 3 ANALYSI 4  We can generalize our observations this L way. That L-value is called a limit. It is found along the y-axis. c ACTIVITY Calculus - is the mathematics of change. MOTIVATION Now, we learned that a limit is actually a y-value. Definition of a limit The limit L is the unique real value that f(x) will approach as x approaches c. In symbols, The limit of f(x) as x approaches c is L. ABSTRACTIO  Limits -backbone of calculus. -the study of limits is necessary in studying change in detail. -the evaluation of a particular limit is what underlies the formulation of the derivative and the integral of a function. ABSTRACTION REMINDERS: For a limit to L to exist, the limits from the left, and the limits from the right must both exist and must be equal to L. ABSTRACTION  There is a left side limit and a right side L limit. Such limits are called one-sided limits. There are standard ways to write the left and right sided limits. For a limit to exist, the left side limit must be c equal to the right side limit. ACTIVITY  EXAMPLE  In symbols, we write it this way:  In symbols, we write it this way:  In conclusion we write this way…. ACTIVITY  In symbols, we write it this way: 2 In symbols, we write it this way: In conclusion, we write this way: ACTIVITY 1  In symbols, we write it this way: 2 In symbols, we write it this way: In conclusion, we write this way: ACTIVITY Is the limit referring to a y- YES value or f(x) ? ! For graphs with a hole- discontinuity, YES does the limit exist? ! ABSTACTION 3 In symbols, we write it this way: In symbols, we write it this way: In conclusion, we write 1 TASK 3 this way: ACTIVITY  What if the left side limit is NOT EQUAL to the right side limit? ACTIVITY TASK 4 In symbols, we write it this way: 5 3 In symbols, we write it this way: In conclusion, we write this way: ACTIVITY whenever, “The left side limit is NOT equal to the right side limit” ABSTRACTION APPLICATION  1 3 DNE APPLICATION  1. ) 2. ) 3. ) 4. ) 5. ) 6. ) APPLICATION  at c = 1, 2, 3 and 4? at integer values of c? at c = 0.4, 2.3, 4.7 and 5.5? at non-integer values of c? APPLICATION  1. ) 2. ) 3. ) 4. ) 5. ) 6. ) APPLICATION  at c = 1, 2, 3 and 4? at integer values of c? at c = 0.4, 2.3, 4.7 and 5.5? at non-integer values of c? APPLICATION EVALUATION EVALUATION  1 DNE -1 DNE 5 EVALUATION  2. 5 DNE 0 1 DNE EVALUATION ENRICHMENT TASK 1 ACTIVITY SHEET TASK 2 ACTIVITY SHEET TASK 3 ACTIVITY SHEET TASK 4 ACTIVITY SHEET