Information for Exam 2
Exam date: Thursday, April 7th
Exam time: 2:00 –
3:00 p.m.
The exam is designed to take
approximately 50 minutes. At 3:00, all
exams will be handed in and we will cover new material for the remainder of the
class period. The exam is a closed book,
mostly closed notes exam (see below). You are encouraged to use a calculator.
Sections: 2.6
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9
Objectives
Section 2.6: You should be
able to:
·
Find the limit of
a function as the variable approaches infinity or negative infinity.
·
Identify when a
function increases or decreases without bound, i.e. has a limit that we say is
equal to positive or negative infinity.
·
Find vertical or
horizontal asymptotes of a function.
Chapter 3: you should be able to
·
State the
definition of the derivative.
·
Find the
derivative using the definition.
There will be exactly one problem like this!
·
Compute
derivatives using the differentiation theorems (the “shortcuts”), including the
product and quotient rules, chain rule, theorems for the trigonometric and
inverse trigonometric functions, rules for exponential and logarithmic
functions.
·
Know when to use
which rule.
·
Use implicit
differentiation when needed.
·
Apply derivatives
to motion problems; understand the relationship among the position, velocity and
acceleration functions.
·
Find the slope of
a tangent line and its equation for a given function.
·
Identify where on
a graph that the derivative does not exist.
You may bring one 8 ½” by
11” page of notes. This page may include definitions, formulas,
explanations, derivative rules. It may
NOT include specific examples. You must
make up your own sheet, put your name on it and hand it in with your exam.
Office Hours:
Thursday,
April 7th: 9:45 –
11:00, 12:30 – 2:00
How to study for this
exam:
Suggested review problems:
Limits involving
infinity :
p. 118 41, 43, 44, 46, 55, 56a
Chapter 3 Review
p. 213 – 217 Practice exercises
1, 7, 9, 11, 17, 19, 26, 31, 41, 45, 47, 49, 57, 65, 71, 73, 76, 93, 94, 99, 101, 103, 113, 119, 120, 121, 135
Additional problem:
Sketch the graph of a
function having the following properties:
a. Its
domain is [-5, 5]
b. It
is continuous on its domain.
c. It
is differentiable everywhere except at x = 0.