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Systemic Initiative Teaching Environment Calculus

Workshop Materials

Limits
Derivatives
Continuity and Differentiability
Lesson Using the List Feature  
Easy Experimenting
Verifying Newton's Law of Cooling
Light Intensity vs. Distance

Lessons

1) Use the CASIO CFX-9850G+ to find the area of the region bounded between the functions: f(x) = x2, g(x) = x + 2

2) Use the CASIO CFX-9850G+ to find the area of the region bounded between the functions:

3) Use the CASIO CFX-9850G+ to find the area of the region bounded between the functions:

4) Understanding equations of lines, slopes, parallel and perpendicular lines can be fun when using the CASIO CFX-9850G+. 

5) Understanding equations of semicircles and parabolas can be fun when using the CASIO CFX-9850G+. 

6) Understanding stepwise continuous functions can be fun when using the CASIO CFX-9850G+. 

7) Investigate graphically the following limit: lim x-> -0.4 ( 5x + 2 ) / ( 5 x² - 13 x - 6 )

8) Investigate graphically the following limit: lim x-> -2 ( x + 2 ) / ( 2 x² + 7 x + 6 )

9) Investigate graphically the following limit: lim x-> Í x² / ( x² - 9 )

10) A young pitcher throws a baseball straight up into the air with a velocity of 100 feet per second.
Because of the gravitational pull of the earth the baseballŒs height above the earth can be modeled by the formula h(x)= 100 x - 16 x2.

11) A model rocketship is fired vertically into the air and reaches a height of 3456 feet in 3 seconds. 

12) From a top a 60 foot overpass, a brick is thrown straight up with a velocity of 20 feet per second. 

13) This simple lesson lets students discover that the derivative of y = e^x is e^x.

14) Apply the Squeeze Theorem in the investigation of lim x-> Í ^{sin x}/_x.

15) Do an analysis of the function g(x) = cos² x - sin x.

16) Do an analysis of the function g(x) = cos² x + sin x.

17) A rubber ball is bouncing straight up and down in such a way that its height above the ground, measured in feet, is given after t seconds by the formula
h(t) = ( 10 | cos t | ) Ì (1 + t)

18) A block of ice slides down a 100 foot chute with an acceleration of 16 ft. / sec2. The distance of the block from the bottom of the chute is given by the formula: 
s(t) = 100 - 20 t - 8 t2

19) Consider the following function: f(x) = x² + 5 x - 3

What are the roots of this function?
Where is the first derivative is 0? Draw the graph of this function and draw the line with slope 5 that is tangent to f(x). 
What is the equation for the tangent line at that point?

20) Consider the following function: f(x) = 5 x³ - 8 x² + x - 2

21) Consider the function f(x) = 3 x⁴ + 8 x³ - 6 x² - 24 x + 10

22) Consider the function: f(x) = 12 - x - x²

23) Consider the function: f(x) = x² - 5 x - 6

What is the area under this function and above the x-axis?

24) Consider the function: f(x) = cos ( x / 2 )

25) Use the CASIO CFX-9850G+ to find the area of the region bounded between the functions: f(x) = 11 - x², g(x) = x² - 4 x + 5

26) Use the CASIO CFX-9850G+ to find the area of the region bounded in the first quadrant of the xy-plane between the functions: f(x) = - 0.75 x + 6, g(x) = - 3 x + 15

27) Use the CASIO CFX-9850G+ to find the area of the region bounded in the first quadrant of the xy-plane between the functions: f(x) = - 1/3 x + 4, g(x) = - x + 8

28) Use the CASIO CFX-9850G+ to find the volume of the solid formed by rotating about the x-axis the region bounded by the x-axis, y = 2, x = 0, and x = 3.

29) Use the CASIO CFX-9850G+ to find the volume of the solid formed by rotating about the x-axis the region bounded by the x-axis, y = x, x = 0, and x = 3.

30) Use the CASIO CFX-9850G+ to find the volume of the solid formed by rotating about the x-axis the region bounded by the x-axis,