October 07, 2013
For each of the following 7 scenarios
sketch y as a function of x
ex. The amount of money in a bank account
earning interest aafo time
aafo: as a function of
October 07, 2013
1. The t
April 24, 2014
One-sided Limits and Delta Epsilon
proofs!
April 24, 2014
Left Hand Limit
in words:
Right Hand Limit
April 24, 2014
Draw a function that satisfies:
April 24, 2014
Make a theorem!
If
c
t
April 30, 2014
Limits Involving Infinity
April 30, 2014
HW Q and A
April 30, 2014
Limits involving infinity are (usually) easy
to evaluate.
But hard to prove!
April 30, 2014
We proved "regular" limits
February 04, 2014
Complex #'s review
Geometric proof of Demoivre's
Theorem
February 04, 2014
Complex Number basics:
i =_
i2=_
complex # = z = a + bi
Notation: Re(z) = the real part of z (a)
Im(z) = th
May 09, 2014
90 second warm up:
Consider:
a) Find the derivative using the "power rule"
b) Now FOIL it out first and find the derivative.
hmmmmmm.
May 09, 2014
We have the following limit memorized:
L
May 05, 2014
What do we already know about the derivative?
May 05, 2014
Consider f(x) = x2 - 8x + 18. Approximate f'(5)
Forward difference quotient
Backward difference quotient
Symmetric difference
August 21, 2013
The Fibonacci Numbers
1170-1250
Quiz Friday on Pascal and Fibonacci
August 21, 2013
Which problems from the hw last
night used the "hockey stick" ?
August 21, 2013
How did you prove 28
August 23, 2013
Quiz Day and Factorials
August 23, 2013
HW qustions from last night:
August 23, 2013
Factorials!
n! =
by definition, 0! =
Right now, factorials are only defined for
whole numbers (thou
August 28, 2013
Geometric and Arithmetic Means
Analysis 2013/14
August 28, 2013
schedule
Tomorrow: Induction!
Friday: Minimum Day Quiz (on
sequences/series and factorials)
Today: Geometric vs. Arithme
September 05, 2013
The Binomial Theorem
Analysis
September 05, 2013
1. Find the coefficient of a6b6 in (2a - b)12
2.
Find the coefficient of x0 in
September 05, 2013
September 05, 2013
From probabilit
May 12, 2014
Quiz topics:
Formal Definition of the derivative:
- at a point
- of a function
Power Rule
Tangent lines
Position, Velocity, Acceleration
Speeding up/slowing Down
May 12, 2014
Why Calculus
May 16, 2014
Antiderivatives Day 2
Quiz debrief
HW presentations 1-5
(students) me 6, 8
Check 9 in partners.
More Anti D's
Ray Sing
May 16, 2014
WARNING!
The only things we know how to differentiate
(
May 07, 2014
Ways of saying "the derivative of f(x)"
1.
2.
3.
To take the derivative is to "differentiate"
May 07, 2014
Warm up:
1. Use the formal definition of the derivative at
a point to find f ' (
April 21, 2014
Approximating the Definite Integral
April 21, 2014
Warm up: (pencils down). Brainstorm a way to
approximate the area of lake Atitlan in Guatemala
(below)
Now do it! (OK, so the units ar
More Quadratics, p.1
First, review from yesterday
Solve for z:
(2 +4i ) z =5 +3i
Some quick questions
1. Solve algebraically using two methods: x 2 +3 x +2 =0
2.
Name all methods in which you can solv
Trig Analyt Honors
Radical & Absolute Value Equations, p.1
Solve the following:
A. 6 x 4 2 x 10
_ is Absolutely_
B.
3x 14 x 6
Did you check to see if both answers work in the original equation? If you
Trig/Analyt Ch2 Review
. . . on an increasing interval AND on a parabolic trajectory !
1.
Use completing the square to prove the quadratic formula.
2.
Determine the function, f(x), where f(x) is a qua
Tt,qf An i.,lr: : ': iragter I
*-,fttll
- t'l',J 5
,
e
r. ttl;
i frt. !/L n il
I
cfw_t| - _*l\ ^\/
,1
-f l
/
=
_q_!Z
*
dqe
(ur*t
,
reecfw_
= JT .t't 5 '/L
un( ef .
!
tb,
tu)_cfw_t = 7'JV a
7JT
q-+ dar
TOP10problemsofChapter1
1. f ( x ) = x and g( x ) =
1
.Find f o g( x ) and g o f ( x ) .Thenfindthedomainofeach.
x2
f ( x ) =
x <2
2 x,
2.Graphthepiecewisefunction
- 2 x +8,
2 x 4
x >4
9 - ( x - 7)
Graph the function: Estimate the intervals on which the function is increasing or
decreasing and any relative maxima and any relative minima.
f x x 2 6 x 5
#43 from HW From a 12cm by 12 cm piece of ca
Greatest Integer & Piecewise, p.1
Explaintoyourgrouphowyouwoulddoeachofthefollowing:
2
1. Solve: 10
2. Expand: ( x 2 ) 3 ( y 2 ) 3
x
FunctionReviewWarmup(Yesthisshouldbereview)
1. In general, a functi
September 06, 2013
September 06, 2013
Consider (2a + b + c + d)11
Find the coefficient of the a5b4c2 term.
September 06, 2013
Sigma Notation
September 06, 2013
HW question 9
September 06, 2013
You can