Review Guide for the MATH 2200 Common Midterm
Fall 2007
The Common Midterm will cover Sections 2.1-2.9 and 3.1-3.2 and will be administered on
Tuesday, October 16 from 6:30-8 p.m. See the following website for more details:
http://math.uwyo.edu/Courses/2200/midterm2007fall.pdf. For the exam, you can bring one
handheld calculator and a 3” x 5” index card. Finally, be sure to bring a photo ID to the exam.
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Know that the slope of the tangent line is the limit of the slopes of the secant lines as the
points used to define the secant line approach the point of intersection between the curve
and the tangent line. Be able to use this to estimate the slope of the tangent line.
Be able to estimate the slope of a tangent line to a curve from data presented in tabular
form.
Be able to determine the limits of functions (from an equation or a graph and by using the
limit laws) or explain why a limit does not exist.
Know and be able to apply the fact that a limit exists only if the left-hand and right-hand
limits are the same.
Know and be able to apply the three criteria necessary for a function to be continuous at a
point, to determine points of discontinuity for functions, to determine intervals on which
functions are continuous, and to determine where functions are continuous from the left
and from the right.
Know and be able to apply the theorem that polynomials, rational, root, trigonometric,
inverse trigonometric, exponential, and logarithmic functions are continuous on their
domains.
Be able to use the Intermediate Value Theorem to argue that for a function f continuous
on [a, b] and for any N between f(a) and f(b), there exists some c in (a, b) such that f(c) =
N.
Be able to determine graphically, algebraically, and numerically limits at infinity and
infinite limits, in addition to recognizing vertical asymptotes as infinite limits and
horizontal asymptotes as limits at infinity.
Be able to determine the slope of a tangent line to a curve at point a using
f ( x)  f (a )
f ( a  h)  f ( a )
lim xa
and by using lim h0
.
xa
h
Be able to determine the equation of the tangent line to a point on a curve.
Be able to find the average and instantaneous velocity of a position function and the
average and instantaneous rate of change of other functions.
Be able to describe the meaning of the derivative in various contexts as well as determine
the units of the derivative.
Be able to regard the derivative as a new function and to determine the derivative using
f ( x  h)  f ( x )
f ' ( x)  lim h0
.
h
Be able to use varying notations for the derivative, including
dy df
d
f ' ( x)  y ' 
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
f ( x)  Df ( x)  Dx f ( x) .
dx dx dx
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Be able to determine higher derivatives, including understanding the context of
position/time functions and their first, second, and third derivatives (velocity,
acceleration, and jerk respectively).
Given a graph of f(x), be able to graph f’(x).
Know and be able to apply the theorem that if f is differentiable at a, then f is continuous
at a. Also recognize that there are functions that are continuous but that are not
differentiable.
Recognize the three cases in which a function can fail to be differentiable: a corner, a
discontinuity, or a vertical tangent.
Be able to use the first derivative to determine where a function is increasing or
decreasing.
Be able to use the second derivative to determine where a function is concave up and
concave down and to identify the points of inflection.
Be able to use the Power Rule, the Constant Multiple Rule, the Sum Rule, the Difference
Rule, and the derivative of the natural exponential function to differentiate constant
functions, power functions, polynomials, and exponential functions.
Be able to use the Product Rule and the Quotient Rule to differentiate functions formed
from other functions by multiplication or division.
Recommended Review Problems:
 Section 2.1: 1, 3, 5, 7
 Section 2.2: 1, 5, 17
 Sections 2.3-2.6
o From the Chapter 2 Review Exercises (p. 176): 1, 5, 7, 9, 11, 13, 19, 21, 23
o From the sections:
 2.4: 16, 33, 38
 2.5: 3, 17, 19, 23, 25, 29, 35, 45
 2.6: 7, 9, 13, 25(a)(b), 27
 Section 2.7: 7, 8, 9a, 10a, 13, 14, 18, 19, 20, 21, 22, 25
o From Review on Page 177: 28ab
 Section 2.8: 19, 20, 21, 22, 41, 42
 Sections 3.1-3.2
o 3.2: 31, 33, 35
o Concept Check on page 255: 1a, b, c, d, e, f, 2a, b,
o From the Chapter 3 Review Exercises (p. 255): 3, 4, 5, 6, 8, 9, 40, 43, 64