Example 1.) Consider the function f (x, y) = 3x x3 2!2 + 3'4
Are there any local maximums, any local minimums?
LUCA/Q M10 and larce may
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Denition.
A. A function of two
Denition. Suppose f has continuous partial derivatives. An
equation of the tangent plane to the surface Z = f(x, y) at the
point P(X0, 30120) is:
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Z - 20 = fx(xo:Jo)(x '" x0) + fy(xo:o
MATH 163 Tangent Planes and Linear Approximations Ch. 11.4
Recall, in calculus one you found the tangent line approximation
of a function of one variable y = f (x) at the point (a, f (1).
L; 2 (on b)
MATH 163 Multiple Integrals Ch. 12.1
Review: The Denite Integral (Calculus 2)
Suppose y = f (x) is a continuous function dened on the interval [a, b].
Also, suppose f (x) Z 0 on [61, b].
To approxim
The Gradient Vector
The directional derivative can also be written as the dot product of
two vectors:
DU (59?): X (X/a\(l l W(X23>\o
: <X(XJ3)IF?(XI?B>. <ailo>
DEA I I o _J
4.; V3(X13\ UL
Denition. If
Rule for Finding Partial Derivatives of z = f (x, y)
Note: When we found a partial derivative it was as if we were
taking the derivative of a function of one variable, the other
variable was regarded
MATH 163 The Ch . R 1 Ch. 11.5
Review. The Chain Rule for functions of a single variable.
Suppose y = f (x) and x = g(t) where f and g are differentiable
functions. _ _.
_L = 3 Hr) a .I cfw_:c x
32$(3
MATH 163 Functions and Surfaces (III. 9.6
Function ofone variable:
it): \RJy k '> i
inpui OULsPLM /
th64 iYdrtd" 46-: )K
Function oftwo variables:
1\P\9> R or i1 \KXRQ YR
Denition. A function of two
MATH 163 Vectors Ch. 9.2
( length)
Denition. A vector is a quantity that has both magnitude and direction.
A vector is often represented by an arrow or a directed line segment.
r3369 71) Magnilwh an 1
MATH 163 Equations of Lines Ch. 9.5
The vector equation of a line L that
1.) points in the same direction as vector 13 (or is parallel to 13 )
2.) Goes through the point P0 with position vector 170
I
~]PI~;~Le~l~
Confronting Development
Assessing Mexico's Economic and Social Policy Challenges
Edited
and
by KEVIN
EDUARDO
J.
MIDDLEBBOOK
ZEPEDA
Sincethe 1980s, Mexico has alternately served as a mod
Math 151 - Taylor Polynomials
Section 1, Page 1 of 10
TAYLOR POLYNOMIALS
The following notes are based in part on material developed by Dr. Ken Bube of the University of
Washington Department of Mathe
MATH 151 Optimization Ch. 4.6
Problem Solving Strategy.
Step 1. Read the problem carefully. As you read jot down important information. What do you know?
What do you want?
Example 1.) A box with a squ
Example 2.) Evaluate the sum,
0 \ a 3
3
Zkz 2: O + \- 4- + 01
- l_1 L~J
k=0 K=O K:\ K:Q K23
. . . 5
Nottce, 1n tins example ck = K
The Taylor polynomial of degree n for the function f (x)
centered at
-ax 6
Example 5.) Find lim xze_2x : Kim X? ' Kim 9.
x-aoo
34:14-22;an ,_ : Op c O
?miLLC+.
u a? 9" ~ ><2
Reap-(1% X e A 65
, Ln A
L X02 $270 U32 LHVUJUL. 1 m alx(xg)
m W 62X
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MATH 163
Calculus III Test 1: Ch. 9.1 - 9.6
Spring 2017
What you can use to study for test 1:
1.) This review sheet
2.) Group assignments
3.) WAMAP homework
4.) In class examples and problems
NOTES: C
MATH 163
Ch. 9.3
The Dot Product
Recall, scalar multiplication:
Example: Calculating the work done by a force.
In calc 2, you calculated the work done by a constant force
F in moving an object a dist
10/12 LP
WarmUp:
In Order to study whether lQ level is related to birth order, data were collected
from a sample of 540 students on their birth order (Oldest/in Between/Youngest)
and their score on an
Lesson Plan 10/10
Warm-Up:
Identify the variables below as categorical or quantitative
.1. Number of cups of coffee consumed per day by SCC students
2. Type of coffee drink ordered at Starbucks
Secti
Negotiation Skills
Our results including the negotiation plan showing the agreed upon set of
accounting alternatives, and reasons in support of the agreement.
My Side: CWN
The purpose of financial sta
6/7/2017 WAMAP Assessment
Checkpoint 8A
Name: Eddy Mahon
#1 Points possible: 5. Total attempts: 3
A teacher is experimenting with a new computer-based instruction and conducts a study to test its
effe
6/1/2017 WAMAP Assessment
Checkpoint 7C
Name: Eddy Mahon
PLEASE READ THESE INSTRUCTIONS BEFORE YOU BEGIN
This Checkpoint is primarily designed to help YOU assess your own understanding of the ideas pr
6/5/2017 WAMAP Assessment
8.1 Introduction to Case C>Q
Name: Eddy Mahon
8.1 Introduction
In previous Topics we performed inference for one variable. More specifically, we learned about inference
for t