Michio Kaku
BY: MAVERICK MAENSIVU AND JACK SUAREZ
Michio Kaku Early Life
He was born in San Jose, California on January 24th, 1927
For a high school project, he built an atom smasher in his parents
garage (probably got an A)
Early Career
Michio Kaku was d
GENERAL EXPANSION OF INTEGRALS OF
R
THE FORM
cosa x sinb xdx
Benjamin Edun
1
ABSTRACT
In this paper, I devise
R a set of equations for generally expanding and solving
integrals of the form cosa x sinb xdx.
2
KEYWORDS
Integral term,absolute integral term.
MATH-119 WEEK 9 RECITATION QUESTIONS 1. Find lim e3/(2x) .
x 2
2. Dierentiate the function y = ek tan 3. Evaluate the integral ex dx x
x
.
4. If f (x) = 3 + x + ex , nd (f 1 ) (4). 5. Solve the following equation for x 2 ln x = ln 2 + ln (3x 4) . 6. Find
Calculus 119 9th Week1 1. Use the subsutitution t =
x2 3 . 2x
3
Since t =
t+
3 2x
+ when x 2 ,
lim e 2x = lim et =
2. d ( x) d k tan x k tan x k tan x d 2 y= (e (k tan x) = e )=e k (sec x) dx dx dx
k 1 x = ek tan x sec2 x 2x 2x 1 3. By using subsutitut
MATH-119
WEEK 10 RECITATION QUESTIONS
1. Compute
a) tan1 (tan 23 )
b) sin cos1 ( 1 ) 3 2. Find the derivative w.r.t x of the function. f (x) = sin1 ( 3. Find the slope of tan1 ( 4. Verify the addition formulas for cosh(x + y ) and sinh(x + y ) 5. Verify
Calculus 119 10th Week1 Recall: 1. 2. 3. 4. 5. 6. sin1 x = arcsin x = y sin y = x where y 2 2 cos1 x = arccos x = y cos y = x where 0 y tan1 x = arctan x = y tan y = x where y 2 2 csc1 x = arccscx = y (|x| 1) csc y = x where 0 < y sec1 x = arcsecx = y (|x
Math 119 Recitation 14
December 22, 2006
1. Evaluate the integral 2. Evaluate
dx . 3 x x2 9 dx 0 x+( x)2 x arctan x (1+x2 )2 0
dx.
3. Test the integral
for convergence.
4. Show that the integral (a) (b)
cos x dx converges 0 x2 +1 sin x x dx converges. 0
10/6/16
Objectives
Identify the three cultures that influence Latin American
music
World Music
Name two types of indigenous music
List the instruments
C ompare and contrast samba and bossa nova
Describe reggae music in terms of musical elements and
social
10/6/16
Name two chordophones common to Middle
Eastern music.
Middle East
D ISCONTINUITIES
Singing of fine poetry
Extensive cultural and
political conflict
Sophisticated melodic improvisation
Compare Jewish and Islamic liturgical music.
Describe the three
suite at least as much as Italian models; German composers often showed a propensity for
elaborate counterpoint. Organ and harpsichord music, inuenced by Sweelinck in the north and
Italian models in the southmFroberger, who contributed to the formation of
10/6/16
Describe the relationship between music and dance
in Native American culture.
Identify the instruments used in Native American
music.
Compare and contrast conjunto and tejano.
List the instruments in a conjunto ensemble.
Compare and contrast C
10/1/2016
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Articulation Agreement by Major
Effective during the 16-17 Academic Year
To: UC Berkeley
|From: Riverside City College
16-17 General Catalog
Semester|16-17 General Catalog
Semester
=
=Computer Science, Lower Division B.A.=
10/1/2016
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1
Articulation Agreement by Major
Effective during the 16-17 Academic Year
To: CSU Los Angeles
|From: Riverside City College
Semester|
Semester
=
=Computer Information Systems - BS=
A total of 120 semester units are required
10/6/16
The unconscious assumption that ones own cultural
background is normal, while others are strange,
exotic, or abnormal.
No rth Ame ri ca
Lati n Ame ri ca
S o u th Asi a (In di a &In do nesi a)
Asi a
M i d d l e E ast
Afri ca
The Epcot Tour
Ethnomus
10/6/16
Elements of Central Asia
Music
Epic Songs
Sung by specially trained bards
Narrations of grand mythic poems
May last from hours to days
Central Asia
Multiphonic singing
Tibet and Mongolia
Vocal technique in which a singer can produce
two or t
10/6/16
WORLD MUSIC
Sound: Common Instruments
Objectives
name the instruments used in Asian music
identify the common elements of melody, harmony,
texture, and rhythm in Asian music
describe the tonal qualities of Beijing opera
explain the concept of ma
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Articulation Agreement by Major
Effective during the 15-16 Academic Year
To: UCLA
|From: Riverside City College
Quarter|
Semester
=
=Computer Science and Engineering/B.S.=
Admission to the Henry Samueli School of Engineerin