Faculty of Management Mathematics Exercises
Sheet 4. Limits and Continuity of Functions - some answers
Exercise 4.1. f) 1 h) 6i) 1/2
j) 1/2 k) 3/2 l)-1/16 m) 1n) 0 o) 1p) e3 q) e r) e−43 Exercise 4.2.
a) lim
x→3−
1
x − 3 = −∞, lim
x→3+
1
x − 3 = ∞ b) lim
x→3−
1
3 − x = ∞, lim
x→3+
1
3 − x = −∞
c) lim
x→3−
1
(3 − x)2 = ∞, lim
x→3+
1
(3 − x)2 = ∞ d) lim
x→1−
x + 1
x − 1 = −∞, lim
x→1+
x + 1 x − 1 = ∞ e) lim
x→2−
1
x2− 4 = −∞, lim
x→2+
1
x2− 4 = ∞ f) lim
x→1−2x−11 = 0, lim
x→1+2x−11 = ∞ g) lim
x→2−4x2−41 = 0, lim
x→2+4x2−41 = ∞ h) lim
x→−2−e4−x21 = 0, lim
x→−2+e4−x21 = ∞ i) lim
x→0−
x
1 + e1x = 0, lim
x→0+
x
1 + ex1 = 0 Exercise 4.3.
Exercise 4.4. a) yes b) no
c) no d) no e) no f) no
Last update: November 15, 2010 1
