ASSIGNMENT 1·5
There are two parts to this assignment. The first part is on WeBWorK — the link is available on the course
webpage. The second part consists of the questions on this page. You are expected to provide full solutions
with complete arguments and justifications. You will be graded on the correctness, clarity and elegance of
your solutions. Your answers must be typeset or very neatly written. They must be stapled, with your name
and student number at the top of each page.
1. Sketch the position, velocity and acceleration graphs of a falling raindrop. Make sure to label your axes
and state your assumptions. You do not have to come up with explicit expressions for your functions,
but you should explain their features (e.g. why a graph is increasing on a particular interval).
2. Let b < a2 . Find the equations of all of the tangent lines to the parabola y = x2 which pass through the
point (a, b).
3. π may be defined to be the number such that the circumference of a circle of radius r is equal to 2πr.
Note that this definition does not make any reference to the area of a circle. In this question, you will
connect the two ideas.
A regular n-gon is a polygon with n equal sides and angles. (For example, a regular 3-gon is a triangle,
and regular 4-gon is a square, a regular 5-gon is a pentagon, and so on.) Explain why the areas of n-gons
inscribed in a circle of radius r get closer and closer to πr2 as n gets larger and larger.
Be careful to avoid circular reasoning in your answer to this question. You may not assume beforehand
that the area of the circle is πr2 .