Math 120: Assignment 5 (Due Tue., Oct. 16 at start of class)
Suggested practice problems (from Adams, 6th ed.):
2.10: 3, 9, 13, 17, 21, 27, 33, 35, 39
2.11: 1, 3, 7, 11, 13, 16-19
3.1: 3, 5, 11, 13, 17, 21, 23, 25, 27, 29, 34
Problems to hand in:
1. Solve the initial value problems
(a) y 0 = x2 − 1/x3 ,
(b)
y 00
= 2 sin(3x),
y(2) = 2
y(0) = 1,
y 0 (0) = 0
2. You are driving at a constant speed of 30m/s when you notice a moose 100m ahead of
you on the road. After a 0.5 second reaction time, you apply the brakes, decelerating
at 10m/s2 . Find expressions for the acceleration, velocity, and position as a function
of time (with time starting when the moose is first sighted). How far do you travel
between spotting the moose and coming to a stop? What is the fate of the moose?
3. Show that f (x) = x4 + x2 + 1 is one-to-one on the domain [0, ∞), and find its inverse
f −1 . What is the domain of f −1 ?
4. Show that f (x) = x3 + 3x2 + 4x + 1 is one-to-one and find (f −1 )0 (9).
5. Show that the function
(
f (x) =
x3
|x|
0
x 6= 0
x=0
is one-to-one, and find its inverse f −1 . At which points is f differentiable? At which
points is f −1 differentiable?
6. Can you find a function which is one-to-one on R but which is not an increasing (or
decreasing) function?
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