Stewart_Calc_7ET ch09sec05
MULTIPLE CHOICE
1. Solve the initial-value problem.
a.
b.
c.
d.
e.
2. Solve the initial-value problem.
a.
b.
c.
d.
e.
3. Solve the differential equation.
a.
b.
c.
d.
e.
4. Solve the initial-value problem.
a.
b.
c.
d.
e.
5. Determine whether the differential equation is linear.
a.
the equation is linear
b.
the equation is not linear
6. In the circuit shown in Figure, a generator supplies a voltage of volts, the
inductance is 2 H, the resistance is 40 , and . Find the current 0.2 s after the
switch is closed. Round your answer to two decimal places.
a.
b.
c.
d.
e.
7. Solve the differential equation.
a.
b.
c.
d.
e.
8. Solve the initial-value problem.
a.
b.
c.
d.
e.
9. Solve the differential equation.
a.
b.
c.
d.
e.
10. Let be the performance level of someone learning a skill as a function of the training
time t. The graph of P is called a learning curve. We propose the differential equation
as a reasonable model for learning, where r is a positive constant. Solve it as a linear
differential equation.
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. Which of the following functions is a solution of the differential equation?
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Solve the initial-value problem.
2. Solve the initial-value problem.
3. Determine whether the differential equation is linear.
4. An object with mass m is dropped from rest and we assume that the air resistance is
proportional to the speed of the object. If is the distance dropped after t seconds, then
the speed is and the acceleration is . If g is the acceleration due to gravity,
then the downward force on the object is , where c is a positive constant, and
Newton’s Second Law gives .
Find the limiting velocity.
5. Solve the initial-value problem.
6. Solve the differential equation.
7. Find the solution of the initial-value problem and use it to find the population when .
