Student Name: _____________________________________

Student ID No.: _____________________________________

University of Toronto
Faculty of Applied Science and Engineering
Quiz Two - MAT197S - Calculus B
Tuesday February 12, 2002     Duration: 50 mins.
Calculators Not Permitted

1. A tank contains 1000 L of pure water at time t=0. Starting at time t=0, the following three things begin to happen:

• A chemical is added to the tank at a linearly increasing rate:
  i.e.
  where f(t) is the rate of chemical added in kg/min
  assume that this chemical is instantly mixed into the entire tank volume
• pure water is added to the tank at a rate of 5 L/min
• the mixed solution in the tank is removed at a rate of 5 L/min

Define y(t) to be equal to the amount of chemical (in kg) in the tank at any time t>0.

a) (2 marks) Find a differential equation representing y(t).

b) (3 marks) Solve fo rthe specific solution for y(t) in terms of k and t.

2. (5 marks) Find all intersection points of the following two polar curves:

3. (5 marks) Evaluate the following integral:

4. Find a general solution to the following differential equation: