University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A30Y 2013-2014
You are expected to work on this assignment prior to your tutorial in the week of Monday
October 21st. You may ask questions about this assignment in that tutorial.
In your tutorial in the week of Monday October 28th you will be asked to write a quiz
based on this assignment and/or related material from the lectures and textbook readings.
TEXTBOOK: Single Variable Calculus, Early Transcendentals, 7e, J.Stewart
READ: Stewart: Sections: 2.2, 2.3, 2.6.
2 Limits and Continuity pages 1-11.
A. Homework problems from the lectures:
1. Investigate the behaviour of f(x) = x near a = 2 by using your calculator to evaluate
the function at values near 2. Does lim x exist? If it does what is it?
2. Write any two deﬁnitions of the following:
(a) lim+ f(x) = ∞ (b) lim+ f(x) = −∞ (c) lim−f(x) = ∞ (d) li− f(x) = −∞
x→a x→a x→a x→a
3. lim (x − 1) sin 1
x→−1 x + 1
Show lim = 1. .