UNIVERSITY OF GHANA
DEPARTMENT OF MATHEMATICS
Take-Home Exercise 1
INSTRUCTION: Answer all questions
Question 1. Find the following limits where they exist:
a) lim [(2x + 1)(x − 3)]
x→0
√
b) lim
x→0
c) lim
x→3
p
3+x−
x
√
3
x2 − 5
2x2 − 6πx + 4π 2
x→π
x2 − π 2
3
1
4t + 8t 3
e) lim
t→2
t+4
d) lim
Question 2. Suppose f (x) and g(x) are two functions and lim = 3 and lim g(x) = −1.
x→a
x→a
Evaluate questions a to c:
a) lim (f (x))2 − (g(x))2
x→a
2f (x) − 3g(x)
f (x) + g(x)
p
c lim −3 g(x)[f (x) + 3]
b) lim
x→a
x→a
d Suppose f (x) =
2
f (x) − f (2)
. Evaluate lim
x→2
x
x−2
Question 3. Show that:.
|h|
.
h→0 h
a) The limit does not exist in lim
h+2
=0
h→∞ 9h2 + 1
b) lim
Page 1 of 2
Question 4. From the accompanying graph of the function g(t), answer the following
questions:
i) lim g(t)
t→0−
ii) lim g(t)
t→0+
vi) lim g(t)
t→2+
vii) lim g(t)
t→2
iii) lim g(t)
t→0
iv) g(0)
v) lim g(t)
t→2−
viii) g(2)
ix) lim g(t)
t→4
Page 2 of 2