Page 93 - Calculus Demystified

CHAPTER 2
80
d sin(x ) Foundations of Calculus
2
(g) e
dx
x
(h) [ln(e + x)]
5. Imitate the example in the text to do each of these falling body problems.
(a) A ball is dropped from a height of 100 feet. How long will it take
that ball to hit the ground?
(b) Suppose that the ball from part (a) is thrown straight down with an
initial velocity of 10 feet per second. Then how long will it take the
ball to hit the ground?
(c) Suppose that the ball from part (a) is thrown straight up with an
initial velocity of 10 feet per second. Then how long will it take the
ball to hit the ground?
6. Use the Chain Rule to perform each of these differentiations:
d
(a) sin(ln(cos x))
dx
d sin(cos x)
(b) e
dx
d
(c) ln(e sin x + x)
dx
d 2
(d) arcsin(x + tan x)
dx
d x
(e) arccos(ln x − e /5)
dx
d
x
2
(f) arctan(x + e )
dx
2
7. If a car has position p(t) = 6t − 5t + 20 feet, where t is measured in
seconds, then what is the velocity of that car at time t = 4? What is the
average velocity of that car from t = 2to t = 8? What is the greatest
velocity over the time interval [5, 10]?
8. In each of these problems, use the formula for the derivative of an inverse
] (1).
function to find [f −1

(a) f(0) = 1, f (0) = 3

(b) f(3) = 1, f (3) = 8
(c) f(2) = 1, f (2) = π 2

(d) f(1) = 1, f (1) = 40