4 2 5 1 3 0011 0010 1010 1101 0001 0100 1011 4 2 5 1 3 0011 0010 1010 1101 0001 0100 1011 Objective: SWBAT examine multiple representations of a function in order to become familiar with properties of common functions DRILL: August 30, 2011 My Expectations of Calculus… •Why did you sign up for calculus? •What do you expect the year to be like? •What are your plans after high school that involve mathematics or science- related fields?
1. Objective: SWBAT examine multiple representations ofa
function in order to become familiar with propertiesof common
functions0011 0010 1010 1101 0001 0100 1011 DRILL: August 30, 2011
My Expectations of Calculus0011 0010 1010 1101 0001 0100 1011 Why
did you sign up for calculus? 1 2 4 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 1 2 4 This lab assignment
can be found on EDLINE.
3. The Dominance of Functions Any exponential function of n
dominates any0011 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
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
13. Objective: SWBAT use direct substitution and otheralgebraic
manipulations in order to evaluate limits0011 0010 1010 1101 0001
0100 1011 DRILL QUIZ #2: September 6, 20110011 0010 1010 1101 0001
0100 1011 1 2 4
14. The Indeterminate Form This limit cannot be determined0011
0010 1010 1101 0001 0100 1011 But this does not mean that the limit
DNE 1 2 When this happens, try the following: Factor 4 Rationalize
the numerator or denominator Use Trig Substitutions to rewrite the
function
17. Objective: SWBAT examine the area of regular polygons in
order to evaluate limits at infinity DRILL QUIZ #3: September 8,
20110011 0010 1010 1101 0001 0100 10110011 0010 1010 1101 0001 0100
1011 1 2 4
18. 0011 0010 1010 1101 0001 0100 1011 1 2 4 This lab
assignment can be found on EDLINE.
19. Horizontal Asymptote0011 0010 1010 1101 0001 a horizontal
The line y = L is 0100 1011 asymptote of the graph of f if or 1 2
4
20. Limits at Infinity of Rational Functions If the degree of
the numerator is less than the0011 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.