Student number
Name [SURNAME(S), Givenname(s)]
MATH 100, Section 110 (CSP)
Week 4: Marked Homework Assignment
Due: Thu 2010 Oct 07 14:00
HOMEWORK SUBMITTED LATE WILL NOT BE MARKED
1. Find g 0 (2) if g(x) = x3 h(cos πx), where h(1) = 2 and h0 (1) = −2.
2. Find the derivative:
(a) y =
s
3
x3 − 1
x3 + 1
(b) x = (1 + t2 ) cos2 t (c) x = (1 + t2 ) cos 2t (d) w =
√
1 + tan z
3. A particle moves along the y-axis so that its position at time t is given by
y = 2 cos(3t + π3 ) (y in cm, t in s).
(a) At t =
(b) At t =
(c) At t =
(d) At t =
2π
,
3
2π
,
3
2π
,
3
2π
,
3
what is the particle’s velocity?
what is the particle’s speed?
in what direction is the particle moving?
is the particle’s speed increasing or decreasing?
4. Find the exact values of the following expressions:
1
(a) sin arcsin
2
,
(b) sin
−1
5π
sin
6
,
2
(c) sec (arctan 10),
(d) cos sin
−1
5. Let f (x) = x2 − 2x, −∞ < x ≤ 1. (a) Sketch the graph of y = f (x) and check that
f is one-to-one. (b) Determine the domain and range of the inverse function f −1 . (c)
Sketch the graph of y = f −1 (x). (d) Find an explicit formula for f −1 (x) (i.e. in terms
of x).
6. Let f (x) = sec x, 0 ≤ x < π/2 or π ≤ x < 3π/2. Note that the domain of f consists of
two disconnected intervals. (a) Sketch the graph of y = f (x) and check that f is oneto-one. (b) Determine the domain and range of the inverse function f −1 . (c) Sketch
the graph of y = f −1 (x). Note that f −1 (x) = sec−1 x, as defined by the textbook on
p. 74.
√ !!
5
.
4