PowerPoint Presentation: Jeopardy! .
PowerPoint Presentation: 100 200 300 400 500 Speed limits “Dah” rivatives Talking continuously Know Your limit Anything goes 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500
Speed limits - 100: Speed limits - 100 Write the expression to compute the average velocity of a position function. Back to game board! or
Speed limits - 200: Speed limits - 200 Back to game board! Write the expression to find the instantaneous velocity of an object. or
Speed limit - 300: Speed limit - 300 Back to game board! Find the average velocity of a particle given the position function below between x =1 and x = 2. y = x 2 Avg. velocity = 2
Speed limit - 400: Speed limit - 400 The velocity function comes from? Back to game board! The derivative of the position function
Speed limit - 500: Speed limit - 500 Find the velocity of a particle with a position function f(t) = 4.9t 2 when t=4 where t is in seconds and f(t) in meters Back to game board! Velocity = 39.2 m/sec
“Dah”rivatives - 100: “Dah”rivatives - 100 Back to game board! How do you find the derivative function of a function?
“Dah”rivatives- 200: “Dah”rivatives- 200 Back to game board! List the notation of a derivative 3 ways
“Dah”rivatives - 300: “Dah”rivatives - 300 Back to game board! A function may fail to be differentiable at 3 types of points A corner (cusp), discontinuity, vertical tangent
“Dah”rivatives - 400: “Dah”rivatives - 400 Sketch the derivative function Back to game board!
“Dah”rivaives- 500: “Dah”rivaives- 500 Back to game board! Find the derivative of y = 2/x
Talking continuously - 100: Talking continuously - 100 Back to game board! Where is this function discontinuous and why At x=0 because
Talking continuously - 200: Talking continuously - 200 Name the 3 criteria for continuity Back to game board! f(a) is defined
Talking continuously - 300: Talking continuously - 300 Where is the function discontinuous? Back to game board! At x = 2
Talking continuously - 400: Talking continuously - 400 Where (if any) are(is) the point(s) of discontinuity? Name the type if discontinuities exist. Back to game board! Infinite discontinuity at x = 0
Talking continuously- 500: Talking continuously- 500 Evaluate Back to game board!
Know your limit - 100: Know your limit - 100 Back to game board! Find the following limit Limit = 14
Know your limit - 200: Know your limit - 200 Back to game board! The exists if and only if
Know your limit - 300: Know your limit - 300 Back to game board! Find the following limit: Does not exist
Know your limit - 400: Know your limit - 400 Back to game board! Find Does not exist
Know your limit - 500: Know your limit - 500 Back to game board! Find the horizontal asymptote for Horizontal asymptote at y = 3/5
Anything goes - 100: Anything goes - 100 Back to game board! Use the Intermediate Value Theorem to show a root exists between x = 1 and x = 2 for the function: f(1)= -1/3 and f(2)= 1/3
Anything goes - 200: Anything goes - 200 Back to game board! Find the following: Positive infinity
Anything goes - 300: Anything goes - 300 Back to game board! Use the squeeze theorem to find the following limit f(x) Limit = 0
Anything goes - 400: Anything goes - 400 Back to game board! Find the following limit Limit = 0
Anything goes - 500: Anything goes - 500 Back to game board! Find the horizontal and vertical asymptotes of Horizontal at Vertical asymptote at x = 5/3