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) = x^{2}, 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. 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 x^{2} - 13 x - 6 )

8) Investigate graphically the following limit:

lim x-> -2 ( x + 2 ) / ( 2 x^{2} + 7 x + 6 )

9) Investigate graphically the following limit:

lim x-> ¥ x^{2} / ( x^{2} - 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 = e^{x} is e^{x}.

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

15) Do an analysis of the function g(x) = cos^{2}
x - sin x.

16) Do an analysis of the function g(x) = cos^{2}
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)

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) = x^{2} + 5 x - 3

20) Consider the following function: f(x) = 5 x^{3} - 8 x^{2} +
x - 2

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

21) Consider the function f(x) = 3 x^{4} + 8 x^{3} - 6 x^{2}
- 24 x + 10

22) Consider the function: f(x) = 12 - x - x^{2}

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

23) Consider the function: f(x) = x^{2} - 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?