FINAL REVIEW MAC 2311-FALL2007
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Finding limit using graphs, numerically, and using the rules
The Squeeze Theorem
Finding limits at infinity (Horizontal Asymptotes), and vertical asymptotes
Know the definition of continuity of a function at a point (on an interval) and be
able to apply the definition to investigate continuity at a point (on an interval)
Know the Intermediate Value Theorem and be able to apply it
Know what it means for a function to be differentiable at a and the relation
between the differentiability and continuity of a function.
Be able to determine from the graph whether a function is differentiable or not at
a point
Functions with discontinuities or piecewise functions with "corners" are good
examples of non differentiable functions. Make sure you know how to graph them
Know the rules for differentiation.
Know how to find the points on the curve where the tangent line is horizontal or,
more generally, the tangent line has a specified slope.
Know how to find the equation of the tangent line at a given point.
Know the product and quotient rules and how to use them.
Review application problems
Know the chain rule and how to use it.
Know how to differentiate a function implicitly and how to find the equation of
the tangent at a given point.
Know how to determine where the curve has a horizontal tangent
Know the derivatives of logarithmic functions and how to use logarithmic
differentiation to take the derivative of very complicated expressions.
Know how to find max/min using first and second derivative test
Know how to set up and solve related rate problem
Know how to set up and solve optimization problem
Do all assigned hw problems from 5.1-5.4
In order to be master of above topics please read lecture notes, do all assigned hw
problems, and review quizzes, and read all other handouts.
Chapter 2
2.2 pages 74 – 76: 3, 6, 12, 14, 16, 22, 24.
2.3 5-32, 33, 35, 41, 44, 51-54, 56, 58, 60, 70, 72, 74, 76, 78, 80(12, 44, 56, 76, 80)
2.4 6, 7-28(all), 30, 35, 36, 37-50(odd), 91, 92, 93 (28, 36, 44, 78, 80)
2.5 8, 18, 20, 25, 40, 44, 46, 50, 62, 70, 72, 73, 74(20, 62, 70)
Chapter 3
3.1 # 4, 8, 14, 16, 18, 22, 32, 34, 38, 40(32, 34, 38)
3.2 # 2, 4, 6, 8, 14, 18, 22, 24, 32, 32, 38, 40, 42, 44, 48, 52, 58(18, 24, 32, 38, 40, 48)
3.3 # 4, 9, 11, 16, 18, 26, 30, 36, 44, 54, 56, 58, 68, 72, 78(44, 58, 72)
3.4 # 6, 18, 22, 26, 30, 34, 50, 60, 68, 72, 82, 86, 92, 102, 106, 115, 122, 123, 124, 128, 132, 134( 34, 82,
124, 132)
3.5 # 2, 4, 6, 8, 10, 12, 19, 22, 26, 30, 32 , 47, 66, 68, 72, 74(10, 32, 72)
3.6# 2, 4, 6, 8, 11, 12, 16, 20, 22, 24, 26, 30, 32, 40, 46(10, 32, 40)
3.7 # 2, 4, 6, 8, 13, 14, 15, 16, 18, 20, 22, 26, 33(16, 20, 32)
Chapter 4
4.1 # 6, 8, 12, 14, 16, 18, 22, 24, 26, 32, 34, 35, 40(16, 34, 40)
Hw7 (due on Nov. 07)
4.2 # 2, 4, 8, 10, 12, 14, 16, 17, 18, 20, 38, 44, 46, 49, 50, 61
4.3 # 4, 6, 8, 20, 24, 34, 36, 46, 49, 84
4.4 # 4, 6, 14, 16, 20, 24, 28, 34, 38, 40, 44, 50
4.5 # 4, 10, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 64, 68
4.6 # 1-4, 5, 8, 10, 12, 18, 21, 28, 30, 39, 44
4.7 # 4, 6, 14, 20, 21, 22, 23, 24
Chapter 5
5.1 # 10, 12, 18, 22, 26, 32, 36, 40, 43
5.2 # 4, 8, 11, 16, 24, 28, 48, 52
5.3 #16, 24, 26, 38
5.4 # 6, 8, 12, 18, 20, 26, 28, 32, 37, 46, 48
Good Luck!