Zhiyu Tian
CNRS, Institut Fourier
Universite de Grenoble I
100 Rue des Mathematiques BP74
38402 Saint-Martin-dH`eres Cedex, France
Email: zhiyu.tian@ujf-grenoble.fr
Employment
Jan. 2015Charge de Recherche, CNRS, Fourier Institute, Grenoble.
Feb. 2015- Apr
Chapter 1 Review/Extra Credit Problems
Remember, no credit will be given for answers without justification.
Problem I
Consider the multivariale function
(
f (x, y)
=
2xy
x2 + y 2
, if (x, y) 6= (0, 0)
, if (x, y) = (0, 0),
0
and the associated differentia
Formulas from Trigonometry
opp y
=
hyp r
adj x
cos=
=
hyp r
opp y sin
tan =
= =
adj x cos
hyp
1
csc =
=
opp sin
hyp
1
sec=
=
adj cos
adj
1
cos
cot =
=
=
opp tan sin
2
2
sin + cos =1
2
2
1+ tan = sec
2
2
1+ cot =csc
(cos(), sin()
sin =
Addition Formul
Harolds Calculus Notes
Cheat Sheet
26 April 2016
AP Calculus
Limits
Definition of Limit
Let f be a function defined on an open
interval containing c and let L be a real
number. The statement:
lim () =
means that for each > 0 there exists a
> 0 such that
Derivative Rules
y
cf
f+g
fg
fg
f
g
f ( g ( x) )
c
xn
ax
ex
log a x
ln x
ln x
sin x
cos x
tan x
csc x
sec x
cot x
y
cf
f + g
f g
f g + f g
f g f g
g2
f ( g ( x) ) g ( x)
0
nx n 1
a x ln a
ex
1
x ln a
1
x
1
x
cos x
sin x
sec 2 x
csc x cot x
sec x tan x
Pre-Calculus 12 (30-1) Formula Sheet
General
Graphing Calculator Format
For ax 2 + bx + c = 0
x=
b
b 2 4ac
2a
For two points (x1 , y1 ) and (x2 , y2 )
d=
(x 2 x 1 )2 + (y2 y1 )2
Exponential and Logarithmic Functions
x: [xmin, xmax, xscl]
y: [ymin, ymax,
Math 31
Calculus II
Formula Sheet for Test 1
February 17, 2015
Product to Sum Formulas:
sin x sin y =
1
(cos(x y) cos(x + y)
2
cos x cos y =
1
(cos(x y) + cos(x + y)
2
sin x cos y =
1
(sin(x + y) + cos(x y)
2
Sum to Product Formulas:
sin x + sin y = 2 sin
9781285057095_AppC1.qxp
2/18/13
8:21 AM
Page C1
C.1
Real Numbers and the Real Number Line
C1
C Precalculus Review
C.1 Real Numbers and the Real Number Line
Represent and classify real numbers.
Order real numbers and use inequalities.
Find the absolute val
1
Calculus I Formulas
MAC 2311
1. Limits and Derivatives
2. Differentiation rules
3. Applications of Differentiation
4. Integrals
5. Applications of Integration
Professor: Dr. Mohammad Shakil
C0-Author: Jeongmin Correa
Mathematics Department
Miami Dade Co
Math 215 Precalculus Review Notes
Formulas
area of circle: A = r2
circumference of a circle: C = 2r
volume of a sphere: V = 13 r3
surface of a right circular cylinder: S = 2r2 + 2rh
volume of a right circular cylinder: V = r2 h
Pythagorean Theorem: In a r
Precalculus Review
Functions to KNOW!
1. Polynomial Functions
Types:
General form
and unique properties
Generic Graph
Constants
Linear
Quadratic
Cubic
Generalizations for Polynomial Functions
- The domain for all polynomial functions is ALWAYS _
- The deg
Lecture 1 : Precalculus Review
Hyperlinks are shown in blue, download the cdf player from the Wolfram Alpha website to view the
Wolfram Alpha interactive demonstrations. When you have downloaded the cdf player, click on
this symbol
to view the demonstrati
2015
Chapter Competition
Target Round
Problems 1 & 2
Name
School
DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO
DO SO.
This section of the competition consists of eight problems, which will be
presented in pairs. Work on one pair of problems will be completed a
Spring Level 5 | 07/31/2010
(1)
Trapezoid ABCD has vertices A( 1; 0), B (0; 4), C (m; 4) and D(k; 0), with
m > 0 and k > 0. The line y = x + 4 is perpendicular to the line containing side CD, and
the area of trapezoid ABCD is 34 square units. What is the
(1)
Spring Level 4 | 07/31/2010
shown?
What is the number of square feet in the area of a triangle with side lengths
14 feet
13 feet
15 feet
(2)
A positive three-digit integer is formed by choosing three dierent digits
from the set f0; 2; 4; 6; 8g. The rs
1
Statistic Questions:
Observational UnitsWho
Five Number
Summery
VariablesWhat
Purpose of researchWhy
LocationWhere
Longitudinal StudiesWhen
Graphing (Required for AP):
1. Always label the X and Y axis
2. Include tittle and units
3. Include a legend or k
EJERCICIO 1
f ( x )=e x
Dominio: cfw_x R
Rango: cfw_ y R y >0
Periodo: No tiene
Continua: S
Montona: S, decreciente.
Positiva o no: S
Par o impar?: impar ninguna.
Puntos mximos: No tiene
Puntos mnimos: No tiene
Para esta funcin usamos el graficador Symbo
OPERACIONES
A = B x,(x A x B).
B A x,(x B x A).
A = B (A B) (B A).
B = cfw_x A | p(x). ESPECIFICACIN
= cfw_x A | x 6= x.
F = cfw_x E | A F, x A.
Ac=cfw_x E | x A.
A B = cfw_x E | (x A) (x B).
A B = cfw_x E | (x A) (x B).
A \ B = cfw_x E | (x A) (x 6 B).
Name
RELEASED FORM
Geometry
H
SE
D
Form H
EA
North Carolina Test of
R
EL
Geometry
Public Schools of North Carolina
www.ncpublicschools.org
State Board of Education
Department of Public Instruction
Division of Accountability Services/North Carolina Testing
Notes
Notes
10 m
Unit 1: Some Basic Figures
Section 1: A Game and Some Geometry
Chapter 01: Points, Lines, Planes, and Angles
How can you find the treasure?
10 m
3. is not the point X.
2. is 10 m (meters) from the building
1. is as far from the fountains
Math 151 (Finite Mathematics)
Midterm I
Last Name:
First Name:
Student Number:
.
Rules of Engagement:
1. Communication between classmates is not allowed.
2. The only materials permitted for the exam are the exam booklet, a writing utensil, and the Sharp E
Math 151, Section 30: Midterm 1
Instructor: Asilata Bapat
October 22, 2013
Name:
This is a 60-minute exam.
Write your solutions in the space provided. Continue on the back if you run out of space.
Show your work. Incomplete work may get partial credit.
Fall 2006 Math 151
Final Exam Practice
(covering Sections 1.1 - 6.5)
courtesy: Amy Austin
NOTE: These problems are to serve merely as practice for
your nal exam. The nal exam for Math 151 is NOT a common exam. Each instructor makes up his or her own nal
e
MATH 151, FINAL EXAM
Winter Quarter, 16 March, 2015
Time: 3 hours, 12:15-3:15
Instructions:
(1) Write your name in blue-book provided and sign that you agree to abide by the
honor code.
(2) The exam consists of 6 questions. The breakdown of points appears