Math 120: Assignment 1 (Due Tues., Sep. 11 at start of class)
1. Find the set of points x satisfying
(a) x3 + x2 ≤ 2x
(b) |3 − 1/x| < 2
2. Find the domain of the function f (x) =
√
2 − x and sketch its graph.
3. Suppose the graph of a function is a straight line passing through points (a, 0) and
(0, b). Does this statement impose any restrictions on the possible values of a and b?
4. Find the limit or explain why it doesn’t exist:
t2 −3t3
t+3t3
√
x
limx→9 3−
x−9
(a) limt→0
(b)
(c) limx→0
(d)
√
x−1
√
2
limt→0 tt
5. A function f is called even if f (−x) = f (x) for all x, and odd if f (−x) = −f (x) for
all x.
(a) Can you find a function which is both odd and even?
(b) Show that any function with domain (−∞, ∞) can be written as the sum of an
odd function and an even function.
(Sep. 8)
1