Casio TEAMS Grant

Systemic Initiative Teaching Environment

Calculus

 

Workshop Materials

Limits Continuity and Differentiability
Derivatives 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:
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3) Use the CASIO CFX-9850G to find the area of the region bounded between the functions:
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4) Understanding equations of lines, slopes, parallel and perpendicular lines can be fun when using the CASIO CFX-9850G. Draw the silhouette of the B-2 Bomber Stealth on the initial viewing screen of the calculator.

5) Understanding equations of semicircles and parabolas can be fun when using the CASIO CFX-9850G. Draw the silhouette of a guitar pick.

6) Understanding stepwise continuous functions can be fun when using the CASIO CFX-9850G. Draw the figure given by using a stepwise continuous function.  Reference points are given.

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-> 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 baseball’s height above the earth can be modeled by the formula h(x)= 100 x - 16 x2.

What is the maximum height that the baseball reaches? How many seconds does it take for the baseball to achieve that height? What is its velocity at that time? What is the velocity of the baseball when it is 126 feet above the ground going up and then again coming down?

11) A model rocketship is fired vertically into the air and reaches a height of 3456 feet in 3 seconds. What is the maximum height that the model rocketship reaches? How many seconds will it be in the air?

12) From a top a 60 foot overpass, a brick is thrown straight up with a velocity of 20 feet per second. How long will it take to hit the ground below? With what velocity will the brick hit the ground? How high did the brick get and how long did it take to achieve that height?

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

14) Apply the Squeeze Theorem in the investigation of lim x-> 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 | ) (1 + t)

What is the velocity of the ball when it hits the ground for the first time. What is the maximum height that the ball attains after that first bounce? What is the approximate velocity of the ball after 28 seconds?

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

How long does it take the block of ice to slide 12 feet? What is the velocity of the block at this point? How long does it take to reach the bottom of the chute?

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

What are the roots of this function? Where is the first derivative is 0?

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

What are the roots of this function? What are the local maximums, local minimums and inflection points of the function?

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

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

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 )

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

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,
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