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 during the week of
Monday Jan. 20th.
In your tutorial in the week of Monday January 27th, 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: 4.5, 4.7, Appendix E.
Notes: 4 Applications of Diﬀerentiation.
A. Homework problems from the lectures :
1. Sketch the graph of each of the functions below showing:
1) domain 2) x, y intersepts
3) symmetry 4) vertical asymptotes
5) horizontal asymptotes 6) slant asymptotes
7) critical points 8) inc/decr intervals , local max/min
9) concavity, inﬂection points10) range
−2 x − 16
(a) f(x) = e−x (b) f(x) = (c) f(x) = ex sinx.
x − 4
2. Given the graph of F = f below, make a rough sketch of the graph of the function
F, with domain R and F(0) = 0. Before you do the sketch make an analysis to ﬁnd
the critical points of F,