MAT136
Test 2 Version A (10:10 am – 12:00 pm )
A1. [2 marks] Write a possible value of b for which the following integral will be an improper integral. If there is no such value, write “Not possible”.
A2. [2 marks] If it converges, evaluate dx and write its value in the box below. If the integral does not converge, write “does not converge”.
A3. [2 marks] Let P(t) be the population of a city in year t. Give an example of a differential equation in which P is proportional to
A4. [2 marks] If the following differential equation is separable, write its general solution. If it is not separable, write in the box “Not Separable”.
A5. [2 marks] Newton’s Second Law of Motion is given by the equation:
where v, the velocity of an object in kilometres per hour, is a function of time t in hours, and k, m, and g are all constants that are bigger than zero. Write an inequality involving v and these constants which implies that v is increasing.
A6. [2 marks] Consider the following system of differential equations, in-volving functions a(t), b(t), and their derivatives:
Write the coordinates of any equilibrium solutions to the above system in the form. (a, b). If there are no equilibrium points, write “No points”.
A7. [2 marks] Consider the series
When you apply the Ratio Test to this series, we let where an is the n
th term in the series. Write in the box below the value of L for the above series.
A8. [2 marks] Let be a convergent series. Does converge or diverge?
If the series converges, write “converge” in the box. If the series diverges, write “diverge” in the box. If there is not enough information to decide, write “not enough info” in the box below.