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 temperature of a cup of hot coffee sitting
on a desk for
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
then
April 24, 2014
Informal definition of a limit:
if a
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 using deltas
and epsilons. Can you remember the
defini
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) = the imaginary part (b)
z = a - bi = the conjugate of z
Fe
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:
Let's prove it!
May 09, 2014
May 09, 2014
Use the limit
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 quotient
nDeriv
Now let's sketch a graph of the deriv
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 28b) and 28c)
August 21, 2013
August 21, 2013
ANOTHER coo
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 (though there are ways to
define them for decimals as well).
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. Arithmetic mean
August 28, 2013
Homework Discussion
Factorials
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 probability you know the formula
for
=
In our text book we define
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 is always in radians:
In our proofs on Friday we "lock
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
(and antidifferentiate) :
power rule
sums, differences
c
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 ' (1/3) if f(x) = 9x3 - 3x2 +6x - 5
2. Sketch f ' (x)
give
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 are
probably a little off!
April 21, 2014
Approximating t
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 solve a quadratic equation.
3.
What is the discriminant? Wh
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 say no, then do it now!
Why must we pay special attent
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 quadratic function with zeros f(2) = f(-4) = 0 and has a y
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-+ darnaty of' fJ
nA^f'l
_
cfw_
t
d omAL
torfl
arrt *f
4t
g/P
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)2 ,
Graphthenewfunction y =2 - 3 f (2 x ) .Describethet
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 cardboard, square corners are cut out so
that the sides c
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 function is a relationship between _ variables (usually _ and
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 evaluate each of these using something
we've learned t