MATE 3021 Practice problems
You are responsible for the problems posted in the syllabus . You do not have
to spend the same amount of time on every problem, but you must
identify groups of problems corresponding to each concept, and you
must spend enough time on as many from each group, as you think is
necessary for you to grasp that concept. On quizzes and tests, you are
graded for carefully justifying the steps, not simply for getting the
right answer. Clusters of problems posted here will be identified by
the posting date; problems posted on, say, Wednesday, are fair game
for an unannounced quiz on the following Monday.
(12/08) (Dates are coded by dd/mm): section 1.2, problems 3--67
of syllabus. Concepts: (i) When are functions equal (ii) Symmetries
(iii) Domain of a function and of the composed of two (or more)
functions.
(13/08) problems 69--78 of section 1.2 (from syllabus). Theme:
(iv) inverse function.
(18/08) problems 1--24 of section 2.1 from syllabus. Topic: (v)
exponential growth.
(21/8) problems 26--66 of section 2.1 from syllabus. Topic: (vi)
recursion.
Problems 5--92 of section 2.2 from syllabus. Topic: (vii) sequences.
(3/09) problems 93--102 of section 2.2 from syllabus. Topic: (viii)
fixed points of recursions.
(10/09) Topic: (ix) limit of functions. Problems 1--32 of section 3.1
from syllabus. For these problems, sketch the graph or obtain it from
graphing software. Go through the steps of the definition given in
class: do horizontal strips of certain radii succeed? Try guessing
whether horizontal strips of arbitrary radius succeed, as this is what
gives the existence of limit.
(18/09) (ix) Limit of functions: problems 38--54 of section 3.1 from
syllabus. For these problems, if you find that the first word you
write is `lim'', take a closer look at your class notes.
(x) Continuity: problems 3--14 of section 3.2 from
syllabus. ``Continuity from the right'' means the right limit exists,
and equals the value of the function. Problems 17--44 from syllabus.
(24/09) (xi) Limits at infinity: problems 1--28 of section 3.3 (from
now on, a range of problem numbers refers to the syllabus; so problems
1--28 comprise 13 problems, not 28). You do not need a graphing
calculator for N(t) of problem 27.
(30/09) (xii) Sandwich theorem, also known as the squeeze theorem. All
problems from the syllabus.
(13/10) (xiii) Definition of the derivative and its geometric
interpretation.
(xiv) Derivatives of powers, sums and polynomials.
(xv) Product and quotient rule. For (xiii)-(xv): all problems from the
syllabus.
(19/10) (xvi) Chain rule.
(xvii) Implicit differentiation. (xvi)-(xvii): pbs 3--71 from
syllabus.
(1/11) (xviii) Higher order derivatives: problems 73--85 from
syllabus.
(xix) Derivatives of trigonometric functions: all problems from
syllabus.
(9/11) (xx) Derivatives of exponential functions: all problems from
syllabus
(18/11) (xxi) Derivatives of inverse and logarithm functions,
logarithmic differentiation. All problems from the syllabus.
(25/11) (xxii) Extrema of functions: problems 1--34 of syllabus.
Last modified: Mon Nov 26 01:19:21 AST 2012