1. Objective: SWBAT examine multiple representations of
a function in order to become familiar with properties
of common functions
0011 0010 1010 1101 0001 0100 1011
DRILL: August 30, 2011
My Expectations of Calculus…
0011 0010 1010 1101 0001 0100 1011
•Why did you sign up for calculus? 1
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•What do you expect the year to be like?
•What are your plans after high school that
involve mathematics or science-related
fields?

2. 0011 0010 1010 1101 0001 0100 1011
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This lab assignment can be found on EDLINE.

3. The Dominance of Functions
• Any exponential function of n dominates any
0011 0010 1010 1101 0001 0100 1011
polynomial function of n.
• Any polynomial function of n dominates and
logarithmic function of n.
• Any logarithmic function of n dominates a
constant term. 1
2
• Any polynomial of degree k dominates a
polynomial of degree l if and only if k>l
4
In general, x(n) dominates y(n) if and only if
grows large.
grows as n

4. Exit Ticket
0011 0010 1010 1101 0001 0100 1011
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5. Homework
0011 0010 1010 1101 0001 0100 1011
Mathematical Autobiography
• Typed
• Double-spaced
• Times Roman, 12 Font
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• 4 paragraphs (as outlined on worksheet)
(one paragraph was done as today’s drill)

6. Objective: SWBAT use area representations in order to
evaluate limits using tables, graphs, and functions
0011 0010 1010 1101 0001 0100 1011
DRILL QUIZ #1: September 1, 2011
0011 0010 1010 1101 0001 0100 1011
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7. 0011 0010 1010 1101 0001 0100 1011
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This lab assignment can be found on EDLINE.

8. Evaluating Limits of Functions
TABLES
0011 0010 1010 1101 0001 0100 1011 GRAPHS
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SUBSTITUTION
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9. Limit Existence from a Graph
Conclusion:
0011 0010 1010 1101 0001 0100 1011
Existence or nonexistence
at x=c has no effect on the
existence of the limit of the
2
function at x=c.
1
4

10. Limit Non-Existence from a Graph
Conclusion:
0011 0010 1010 1101 0001 0100 1011
The limit at x=c does not exist
if the function has oscillating
or unbounded behavior or a
2
jump discontinuity at x=c.
1
4

11. Exit Ticket
0011 0010 1010 1101 0001 0100 1011
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12. Homework
0011 0010 1010 1101 0001 0100 1011
Calculus Textbook
• Pgs. 54-58
• #’s 2, 7, 8, 9-18, 20, 26, 60, 63, 65, 66
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• Pg. 67
• Choose one from #’s 11-22

13. Objective: SWBAT use direct substitution and other
algebraic manipulations in order to evaluate limits
0011 0010 1010 1101 0001 0100 1011
DRILL QUIZ #2: September 6, 2011
0011 0010 1010 1101 0001 0100 1011
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14. The Indeterminate Form
• This limit cannot be determined
0011 0010 1010 1101 0001 0100 1011
• But this does not mean that the limit DNE
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When this happens, try the following:
• Factor
4
• Rationalize the numerator or denominator
• Use Trig Substitutions to rewrite the function

15. Exit Ticket
0011 0010 1010 1101 0001 0100 1011
Evaluating Limits
Worksheet
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16. Homework
0011 0010 1010 1101 0001 0100 1011
Calculus Textbook
• Pgs. 67-69
• #’s 24, 27, 35, 42, 44, 52, 54, 65, 67, 70, 77,
97, 98
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• Prove the 2nd Special Trig Limit involving
cosine

17. Objective: SWBAT examine the area of regular
polygons in order to evaluate limits at infinity
DRILL QUIZ #3: September 8, 2011
0011 0010 1010 1101 0001 0100 1011
0011 0010 1010 1101 0001 0100 1011
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18. 0011 0010 1010 1101 0001 0100 1011
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This lab assignment can be found on EDLINE.

19. Horizontal Asymptote
0011 0010 1010 1101 0001 a horizontal
The line y = L is 0100 1011 asymptote of the graph of f if
or
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20. Limits at Infinity of Rational Functions
• If the degree of the numerator is less than the
0011 0010 1010 1101 0001 0100 1011
degree of the denominator, then the limit of
the rational function is 0.
• If the degree of the numerator is equal to the
1
degree of the denominator, then the limit of
2
the rational function is the ratio of the leading
coefficients.
4
• If the degree of the numerator is greater than
the degree of the denominator, then the limit
of the rational function does not exist.

21. Exit Ticket
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22. Homework
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Calculus Textbook
• Pgs. 205-207
• #’s 1-8, 15-20, 88b
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