PART 1:
Problem 1a: Given the distance covered by a body as a function of time find the velocity and acceleration.
Problem 1b: Given the acceleration of a body as a function of time find the distance and velocity (Also, find the area under a curve)
Problem 1c Given the velocity of a body as a function of time find the distance.
Problem 2: Find the tangent to a curve (Related to 1a)
Problem 3: Find maxima and minima of a function.
Problem 4: Find the length of a curve
Exercise 1: What tools of calculus you would use to solve each of these problems?
Exercise 2: How would you solve each of these problems without calculus?
Simulation illustrating the law of large numbers. Each frame, a coin that is red on one side and blue on the other is flipped, and a dot is added in the corresponding column. (Source: Wikipedia)
Another illustration of the Law of Large Numbers can be found here.
Part 2: Find the tangent to the parabola f(x)= 3 x^2 - x at the point P=(1,2).
