1 h 9 e $ s i n t h e o r y, a p p l i c a t i a n
|
|
- Marilynn King
- 4 years ago
- Views:
Transcription
1 T : 99 9 \ E \ : \ \ \ \ \ - \ \ T \ \ \ : \ 99 9 T : E : / T V 9 \ E \ \ : 4 \ 7 8 / T \ V \ 9 T - w - - V w w - T w w \ T \ \ \ w \ w \ - \ w \ \ w \ \ \ T \ w \ w \ w \ w \ \ w \ \ \ - - w T w \ T w w j - V - - W 75 U w T U W w F - \ T C C w \ \ V ˆ - w - T w T x w T - j \ [ ˆ - - T ˆ w w w ˆ ˆ w ˆ w w T ˆ x ˆ w w w w w ˆ w w ˆ w T w w ˆ w ˆ j w ˆ 6 J T w 6 J - - W U ˆ ˆ T W ˆ F ˆ W C C \ - 4 \ - w Kw w \ Kw - - w \ - - \ x C \ C C -: 6 46 w \ \ C : w \ \ ˆ ˆ ˆ ˆ j67 87 ˆ Q ˆ ˆ ˆ T ˆ - ˆ ˆ T ˆ ˆ w \ 85 C : J j 8 T Q z w G Q 85 Q XX T 8 8 \ 8 V 6 z C : T 5 Q U z-w G 5 8 W 68 Q XX 94 w w \ Ex V - z \ w \ w - U - W \ \ \ w \ - w Ex w w \ j w - w j w - \ w Kw \ \ w w \ - \ w w x x \ - \ \ T T \ C w T T \ - C : : \ 6 46 w \ * E - : w w - \ T 64 T 7 V \ V \ \ \ \ j \ 8 7 8
2 \ V T w w w \ T w w w w T ˆ x z T j \ \ ; \ \ ; \ \ \ \ \ \ ; \ \ \ \ \ \ \ \ \ \ \ x w w \ \ T \ Ex z \ \ \ \ \ \ \ \ \ \ T \ V \ \ V T w j w w T w j w w w w - w T - w x z w T j w x w w w w w w z T w Ex w z w T V 9 V T - w j w w T - w j w w w w w T [ x z w T j ; ; ; ; ; - ; ; w ; ; x w - w w w w w w z T w Ex w x z - W x w ; - ; ; ; T V 9
3 x z w w / w - - F x - w z - w - T x - x T w w F w w w - w T x - z T w w w w - w W - w T w - - w - w w x xt [ T [ w w w w x - w
4 \ x \ \ \ x \ \ x \ T V \ 9 \ \ \ - z \ \ - \ w - \ \ - w - \ - \ \ \ \ \ - \ w \ \ w - F x - \ \ w \ \ \ \ - w \ - \ \ w \ - - \ \ ˆ z w - \ T - - \ \ x \ - \ \ \ \ - \ \ - ˆ w \ - - x \ \ z T w \ - - w - \ w \ T - \ - -- x \ F- w w \ \ - w \ \ \ \ x \ \ \ \ T \ \ w w w F ˆ w T x \ w \ z \ \ T \ \ w w w w w T w x z \ T W w w T \ \ w w w w \ w w x ---x T- - w \ - -
5 V [ z x x - z w T w w w C w x [ - - w 5 C x E C x w [ : j w w x Ex w / x w w x C x w w w [ C C x - w w w [ - w F z [ F x w x w x T - - T w - - x - w x [ - w w w T - x - T - w - w
6 V \ - -- V \ - w z ö ö - 4 \ T 4 V \ 9 4 z x x x x z z w \ T T w w w \ w w x [ \ \ w w x \ - 5 \ C - w x ˆ E C 5 x ˆ C w x -- w -- -E C x- w w w x : \ Ex w / x w w x x Ex C x w ˆ w w x ˆ w w C C x w w w [ x C x w F ˆ - -w w - w w C w x w x \ -w w- -w w T w x w \ - - -F x w z [ \ w w \ T x \ w w x \ w - x - - \
7 T T j w x j x w x w w w T T x x w w z w w - [ T x w w - z [ x w z x [ 6 / w w j T x w - w w x z F x w [ w w V F T T j T C F U C T w T w - - w T [ x w - - z - z w K - C w w T x x j U U C U
8 \ T T j w - \ - \ - \ U w w [ T T j w \ - - \ w w \ \ x \ T \ \ T \ x H - F x - H w \ \ x \ \ T V 9 5 w - x \ w - ˆ w \ - - \ w ˆ x w w w x T T T x x x \ x ˆ w w w T x w - w - - w w ˆ z \ T x w w x w - - z w z x \ 6 \ w z x / w 6 w \ T j x w T w w xz F ˆ x w [ w w- x-z - - F- - - w - --x - - w w w \ \ w V F w T V F \ T T T j T C F U C T T w w C F U C T w w T T [ \ w x w \ z w
9 V T z w : G T C ww T w w w [ w - - w - F [ x C x T x - w - T - w T w w w [ - x - w - j z w x z T x x w - w T x x w w w x [ T j w j x w z w - w z [ w - w w w T w x w T w
10 V \ T V z w [ \ w \ T w j - z T C w T w C C C w w T ˆ -w w- - T w F w w w w w - w [ w - w T V 9 6 -w w F C C T x T w x w \ T T w w T w T w ˆ ˆ w w w- - w -- w - - x - - x w \ j w j x x z \ w x z w \ \\ \ T x x w w w - x x w w w w x ˆ [ x \ T j x x w w w- -x w w z w z w w w T T j w w w x T w w z w w w C
11 w w C C T C C w - - w w w C C w T [ - w T w [ w w w T x - C w w w T x w w T x z x w w w - - H - x w x [ w x x x w x w x T C T T j x w x T j w w - w T - w j w w w T j w E w T j w x w w w T T / z w j w w T j
12 \ w- - \ \ \ T / w w - w / \ w ˆ \ C \ T j : / / w w w w / w / j / w T - w C C T T V 9 7 C C T C C w C C w w w w w C C w w w T C C [ \ \ w T w w -w - - w T C w w w T w w w T x x z C \ x w w T x \ \ w \ w T x z x --x ˆ x w w w w x w - - x x w x w \ \ T C T -x -- T j x w - w x w w x w w x w x T x w j w x w w T C T T j x T j w w E w x x j w w w T T w / \ T z w j w w T j T / \ w
13 V T j / w F T W w T j w w j [ V V G w Y 6 [ V K w C F C 66 wy [ K T z C z H [ 4 - Y z [ 5 H Q K Q : 9 / 5 [ 6 J Z T w : T G T F w T w / - - [ 7 W H Z Y J Y H G : E E : / 4 [ 8 C K W 5 G z U T - E z : 98/ [ 9 V J C T 46 [ T T C w w T E w [ V T T C - - J C T z [ Tw W H w 84 : / 8 4 [ C [ 4 C z : W C C : / [ 5 H H Y F : 8 / [ 6 K F K z Q x : 9 / / [ 7 G K W E V V Q C 76 : 8 / 7 [ 8 Y F G - j :
14 V \ T V j T : 6 / j 8 [ 9 F \ G \ G T Y Y j z- z w - T V 9 8 F T T W W w w T j w j \ \ \ \ V V - [ \ V -- V G - w Y 6 G \ V w Y K w [ V \ -- \ K - \ C F \ \ C - 66 \ C wy F C 66 K T \ wy \ - z - z - H [ K T \ \ z C \ 4 \ H \ \ \ \ Y z [ \ 9 \ \ \ 5 H Q \ z K \ : [ 5 H \ 5 Q K \ Q 6 J \ Z T - w : T G - w \ - T - w- [ 6 J Z T \ 99 9 \ w : T G 478 w \ 7 W H Z Y J \ Y- H G \ : E T E - w \ - \ 578 \ \ : 4 \ / C K W 5 G- z U [ 7 \ W \ H Z \ E - Y - \ - J - -z \ 96 \ 9 H - \ G \ : \ E E : \ : 9 / V J [ 8 C C T K \ - - \ W 4 ˆ 5 6 z U - T \ T C \ E w z w T \ \ 84 E 847 w- - : 9 8 / [ 9 V \ V- \ - T T C J -J - C - T - - C T 4 6 [ \ \ \ \ Tw W - H - \ \ w w \ \ T w - 84 ˆ - \ E \ : \ - - \ \ [ \ - 7 V 6 \ \ T 4 T C C - W \ \ \ J C C T 7 \ 9 z
15 \ - T \ - \ 8 \ 9 99 \ T \ T \ 99 - \ 478 / \ \ T Q V [ 478 / T Q V Q H J K E H J K - E : J -J [ \ \ 4 \ 9 4 : 94 T5 / Q j V 9 5 : 94 5 j 9 5 Q \ H \ [ C Y E F w H Y C Y F - w : T\ Ex C H : H Y T Ex C - H - J : \ T : : : \ / j - T 9 5 [ H T C V G - [ C \ Y \ F z w w\ w H : T H T - C 7 : 99 \ : V G C [ \ FX : z - F T z w w \ T / - - T - 7 w : T - 99 : 478 [ H \ 48 T 57 \ \ 99 \ 478 \ C - \- FX z- F [ 5 J - V G \ C z - \ w w T - T \ 79 : 99-9 : / - 99 T \ 7 \ 99 [ 6 z 4 Q : 478 w 5 j -- - : T 9 - T - [ 99 - \ - : FX z \ F 99 [ 7 F X z V - C 478 J \ / 5 J \ : T T 47 \ \ \ \ / / T [ 8 W H V K C 8 79 \ 99 9 [ 4 C w : 4 \ 7 8 C \ : \ T : 6 4 z 7 Q T \ j : 478 / : - T \ [ 9 E 9 K48 C 57 \ : T F X z V- C [ 5 - \ J 99 \ 47 8 / - - [ K : F V - T : \ \ T - 9 w : z \ 99 9 \ 8 \ : 4 W 7 8 H / V T V 9 9 K - - C [ 6 C \ z Q - : - T 5 - \ - 7 \ : T 99 9 \ 9 \ : : 478 E - -K C [ 7 \ F X - z - V T C - \ J 86 \ - 99 / 47 \ 8 : T \ 4 \ K F \ V : / T - -w 9 [ 8 W \ H \ - 99 V K : -z 478 \ T V \ 9 \ 9 C \ C \ \ : 4 7 \ \ \ 99 9 : \ 478 / [ 9 \ E \ K C \ T 7 86 \ / \
MANY BILLS OF CONCERN TO PUBLIC
- 6 8 9-6 8 9 6 9 XXX 4 > -? - 8 9 x 4 z ) - -! x - x - - X - - - - - x 00 - - - - - x z - - - x x - x - - - - - ) x - - - - - - 0 > - 000-90 - - 4 0 x 00 - -? z 8 & x - - 8? > 9 - - - - 64 49 9 x - -
P A L A C E P IE R, S T. L E O N A R D S. R a n n o w, q u a r r y. W WALTER CR O TC H, Esq., Local Chairman. E. CO O PER EVANS, Esq.,.
? ( # [ ( 8? [ > 3 Q [ ««> » 9 Q { «33 Q> 8 \ \ 3 3 3> Q»«9 Q ««« 3 8 3 8 X \ [ 3 ( ( Z ( Z 3( 9 9 > < < > >? 8 98 ««3 ( 98 < # # Q 3 98? 98 > > 3 8 9 9 ««««> 3 «>
Neatest and Promptest Manner. E d i t u r ami rul)lihher. FOIt THE CIIILDIIES'. Trifles.
» ~ $ ) 7 x X ) / ( 8 2 X 39 ««x» ««! «! / x? \» «({? «» q «(? (?? x! «? 8? ( z x x q? ) «q q q ) x z x 69 7( X X ( 3»«! ( ~«x ««x ) (» «8 4 X «4 «4 «8 X «x «(» X) ()»» «X «97 X X X 4 ( 86) x) ( ) z z
II&Ij <Md Tmlaiiiiiit, aad once in Ihe y a w Teataa m i, the vmb thatalmta oot Uiaapirit world. into as abode or wotld by them- CooTBOtioa
382 4 7 q X
Wayfarer Traveler. The. Laura. Most of us enjoy. Family and multi-generational travel. The Luxury of Togetherness. Happy Traveling, Owner s
6, z j Kw x w 8- x - w w w; x w w z, K, x -, w w w, w! x w j w w x z w w J w w w, w w w x w w w w 6, w q, w x, w x x, w Q, w 3-, w,, -w 6 ;, w x w w-- w j -, -, x, - -,, -,, w,, w w w, w w w, - w, w,,
s f o r s o l v i n g t h e n o n l i n
M M R M q q D O : q 7 8 q q q M q x- q M M M 9 R R D O : 78 / x q D MO : M 7 9 8 / D q P F x z M q M q D T P - z P G S F q q q q q q q D q q PZ w - z q - P q q q w q q q w q q w z q - w P w q w w - w w
Sect Least Common Denominator
4 Sect.3 - Least Common Denominator Concept #1 Writing Equivalent Rational Expressions Two fractions are equivalent if they are equal. In other words, they are equivalent if they both reduce to the same
LOWELL WEEKI.Y JOURINAL
/ $ 8) 2 {!»!» X ( (!!!?! () ~ x 8» x /»!! $?» 8! ) ( ) 8 X x /! / x 9 ( 2 2! z»!!»! ) / x»! ( (»»!» [ ~!! 8 X / Q X x» ( (!»! Q ) X x X!! (? ( ()» 9 X»/ Q ( (X )!» / )! X» x / 6!»! }? ( q ( ) / X! 8 x»
LOWELL WEEKLY JOURNAL. ^Jberxy and (Jmott Oao M d Ccmsparftble. %m >ai ruv GEEAT INDUSTRIES
? (») /»» 9 F ( ) / ) /»F»»»»»# F??»»» Q ( ( »»» < 3»» /» > > } > Q ( Q > Z F 5
ECONOMICS 207 SPRING 2006 LABORATORY EXERCISE 5 KEY. 8 = 10(5x 2) = 9(3x + 8), x 50x 20 = 27x x = 92 x = 4. 8x 2 22x + 15 = 0 (2x 3)(4x 5) = 0
ECONOMICS 07 SPRING 006 LABORATORY EXERCISE 5 KEY Problem. Solve the following equations for x. a 5x 3x + 8 = 9 0 5x 3x + 8 9 8 = 0(5x ) = 9(3x + 8), x 0 3 50x 0 = 7x + 7 3x = 9 x = 4 b 8x x + 5 = 0 8x
A. H. Hall, 33, 35 &37, Lendoi
7 X x > - z Z - ----»»x - % x x» [> Q - ) < % - - 7»- -Q 9 Q # 5 - z -> Q x > z»- ~» - x " < z Q q»» > X»? Q ~ - - % % < - < - - 7 - x -X - -- 6 97 9
LOWELL WEEKLY JOURNAL
Y -» $ 5 Y 7 Y Y -Y- Q x Q» 75»»/ q } # ]»\ - - $ { Q» / X x»»- 3 q $ 9 ) Y q - 5 5 3 3 3 7 Q q - - Q _»»/Q Y - 9 - - - )- [ X 7» -» - )»? / /? Q Y»» # X Q» - -?» Q ) Q \ Q - - - 3? 7» -? #»»» 7 - / Q
LOWHLL #WEEKLY JOURNAL.
# F 7 F --) 2 9 Q - Q - - F - x $ 2 F? F \ F q - x q - - - - )< - -? - F - - Q z 2 Q - x -- - - - 3 - % 3 3 - - ) F x - \ - - - - - q - q - - - - -z- < F 7-7- - Q F 2 F - F \x -? - - - - - z - x z F -
Name: Class: Date: = 30.6 and t 15. = 125 D. t 21 = 20 = 3.75, S 6
Class: Date: Mock Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Two terms of an arithmetic sequence are t = 0.6 and t 1 = 89.6. What is t
3.1 Symmetry & Coordinate Graphs
3.1 Symmetry & Coordinate Graphs I. Symmetry Point symmetry two distinct points P and P are symmetric with respect to point M if and only is M is the midpoint of PP' When the definition is extended to
oenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our
x V - --- < x x 35 V? 3?/ -V 3 - ) - - [ Z8 - & Z - - - - - x 0-35 - 3 75 3 33 09 33 5 \ - - 300 0 ( -? 9 { - - - -- - < - V 3 < < - - Z 7 - z 3 - [ } & _ 3 < 3 ( 5 7< ( % --- /? - / 4-4 - & - % 4 V 2
Sections 4.1 & 4.2: Using the Derivative to Analyze Functions
Sections 4.1 & 4.2: Using the Derivative to Analyze Functions f (x) indicates if the function is: Increasing or Decreasing on certain intervals. Critical Point c is where f (c) = 0 (tangent line is horizontal),
LOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort
- 7 7 Z 8 q ) V x - X > q - < Y Y X V - z - - - - V - V - q \ - q q < -- V - - - x - - V q > x - x q - x q - x - - - 7 -» - - - - 6 q x - > - - x - - - x- - - q q - V - x - - ( Y q Y7 - >»> - x Y - ] [
Math RE - Calculus II Antiderivatives and the Indefinite Integral Page 1 of 5
Math 201-203-RE - Calculus II Antiderivatives and the Indefinite Integral Page 1 of 5 What is the Antiderivative? In a derivative problem, a function f(x) is given and you find the derivative f (x) using
MATH443 PARTIAL DIFFERENTIAL EQUATIONS Second Midterm Exam-Solutions. December 6, 2017, Wednesday 10:40-12:30, SA-Z02
1 MATH443 PARTIAL DIFFERENTIAL EQUATIONS Second Midterm Exam-Solutions December 6 2017 Wednesday 10:40-12:30 SA-Z02 QUESTIONS: Solve any four of the following five problems [25]1. Solve the initial and
HOMEWORK 4 1. P45. # 1.
HOMEWORK 4 SHUANGLIN SHAO P45 # Proof By the maximum principle, u(x, t x kt attains the maximum at the bottom or on the two sides When t, x kt x attains the maximum at x, ie, x When x, x kt kt attains
A n.. a l y.. s i s.. a n.. d.. G.. e.. o.. m.. e.. t r y.. i.. n.. M.. e t r i c.. S.. p a.. c e.. s \ centerline
G O I : 4 8 G 3 v- G G 6 9 4 O I : 4 8 / 3 v O I : G 4 3 8 / 6 94 3 v G 3 9 4 - J K w * w - J K v w w : - - v - - w wv w w - F I6 FI F 6 Uv w F Uv ˆ v v ˆ wv wk W w - - : W w - v - w v w H w - v w v 8
A DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any
Y Y Y X X «/ YY Y Y ««Y x ) & \ & & } # Y \#$& / Y Y X» \\ / X X X x & Y Y X «q «z \x» = q Y # % \ & [ & Z \ & { + % ) / / «q zy» / & / / / & x x X / % % ) Y x X Y $ Z % Y Y x x } / % «] «] # z» & Y X»
David Burns and Matthias Flach. t y
4 Dv B F v 4 b Dv 4 B Dv B F v b F bk bk R F R q v q b R F L L - b q q - Eq: L T C O b q ˆ bk bk * T C O b TΩ bk + ψ T Ω bk T Ω T C T O bk bk + ˆ O w w ψ * R ˆ R T bk Ω bk T O ˆ w R k R bk bk R T C O bk
z 2 = 1 4 (x 2) + 1 (y 6)
MA 5 Fall 007 Exam # Review Solutions. Consider the function fx, y y x. a Sketch the domain of f. For the domain, need y x 0, i.e., y x. - - - 0 0 - - - b Sketch the level curves fx, y k for k 0,,,. The
Polynomial functions right- and left-hand behavior (end behavior):
Lesson 2.2 Polynomial Functions For each function: a.) Graph the function on your calculator Find an appropriate window. Draw a sketch of the graph on your paper and indicate your window. b.) Identify
Problem 1 HW3. Question 2. i) We first show that for a random variable X bounded in [0, 1], since x 2 apple x, wehave
Next, we show that, for any x Ø, (x) Æ 3 x x HW3 Problem i) We first show that for a random variable X bounded in [, ], since x apple x, wehave Var[X] EX [EX] apple EX [EX] EX( EX) Since EX [, ], therefore,
JUST THE MATHS UNIT NUMBER PARTIAL DIFFERENTIATION 1 (Partial derivatives of the first order) A.J.Hobson
JUST THE MATHS UNIT NUMBER 14.1 PARTIAL DIFFERENTIATION 1 (Partial derivatives of the first order) by A.J.Hobson 14.1.1 Functions of several variables 14.1.2 The definition of a partial derivative 14.1.3
Algebra I CP Final Exam Review
Class: Date: Algebra I CP Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the graph that displays the height of a ping pong
LB 220 Homework 4 Solutions
LB 220 Homework 4 Solutions Section 11.4, # 40: This problem was solved in class on Feb. 03. Section 11.4, # 42: This problem was also solved in class on Feb. 03. Section 11.4, # 43: Also solved in class
1871. twadaa t, 30 cta. pat Haa;fe,ttaw Spiritism. From Uis luport of tie vision, and in U e n i e h t i a d i W A C h r f i
V < > X Q x X > >! 5> V3 23 3 - - - : -- { - -- (!! - - - -! :- 4 -- : -- -5--4 X -
Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review
Name: Class: Date: Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review 1 Write 3x 2 ( 2x 2 5x 3 ) in standard form State whether the function is even, odd, or neither Show your work
LOWELL WEEKLY JOURNAL
W WY R G «( 5 R 5 Y q YG R ««W G WY Y 7 W \(\ 5 R ( W R R W ) W «W W W W< W ) W 53 R R Y 4 RR \ \ ( q ) W W X R R RY \ 73 «\ 2 «W R RG ( «q ) )[ 5 7 G ««R q ] 6 ) X 5 5 x / ( 2 3 4 W «(«\Y W Q RY G G )
Sect Polynomial and Rational Inequalities
158 Sect 10.2 - Polynomial and Rational Inequalities Concept #1 Solving Inequalities Graphically Definition A Quadratic Inequality is an inequality that can be written in one of the following forms: ax
R for beginners. 2 The few things to know before st. 8 Index 31
; & & & 8 * ( 0 " & 9 1 R f Eu l 1 W R? 3 T fw kw f 5 3-4.1 T
Tracing High-z Galaxy Kinematics
T H- Gxy K v b k q Ey Wk THE KMOS 3D TEAM PI: NM Fö Sb D W, JT M, S Wy, E Wy, K B, A B, R B, G B, J C, R Dv, M Fb, M F, R G, S Kk, J Kk, P L, D L, I Mv, E N, D R, R S, S S, LJ T, K Tk, P v Dkk, + I C T!
CITY OF LAS CRUCES INFRASTRUCTURE/CIP POLICY REVIEW COMMITTEE
1 5 6 7 8 9 11 1 1 1 15 16 17 18 19 0 1 6 7 8 9 0 1 5 6 7 8 9 0 1 ITY OF L U IFTUTU/I OLIY VI OITT T fwg f g f f L - If/I w f b 17, 018 :0.., f L,, bg (f 007-), 700, L, w x. B T: Gg,, G g, / T, 5 J, g,
Test one Review Cal 2
Name: Class: Date: ID: A Test one Review Cal 2 Short Answer. Write the following expression as a logarithm of a single quantity. lnx 2ln x 2 ˆ 6 2. Write the following expression as a logarithm of a single
25. Chain Rule. Now, f is a function of t only. Expand by multiplication:
25. Chain Rule The Chain Rule is present in all differentiation. If z = f(x, y) represents a two-variable function, then it is plausible to consider the cases when x and y may be functions of other variable(s).
T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r )
v e r. E N G O u t l i n e T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) C o n t e n t s : T h i s w o
Algebra 2 Honors: Final Exam Review
Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt
First Order Differential Equations
Chapter First Order Differential Equations Contents. The Method of Quadrature.......... 68. Separable Equations............... 74.3 Linear Equations I................ 85.4 Linear Equations II...............
Chain Rule. MATH 311, Calculus III. J. Robert Buchanan. Spring Department of Mathematics
3.33pt Chain Rule MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Spring 2019 Single Variable Chain Rule Suppose y = g(x) and z = f (y) then dz dx = d (f (g(x))) dx = f (g(x))g (x)
AP Calculus AB Unit 3 Assessment
Class: Date: 2013-2014 AP Calculus AB Unit 3 Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. A calculator may NOT be used on this part of the exam.
GEOMETRY UNIT 1 WORKBOOK. CHAPTER 2 Reasoning and Proof
GEOMETRY UNIT 1 WORKBOOK CHAPTER 2 Reasoning and Proof 1 2 Notes 5 : Using postulates and diagrams, make valid conclusions about points, lines, and planes. I) Reminder: Rules that are accepted without
I.G.C.S.E. Similarity. You can access the solutions from the end of each question
I.G.C.S.E. Similarity Inde: Please click on the question number you want Question 1 Question Question Question 4 Question 5 Question 6 Question 7 Question 8 You can access the solutions from the end of
STAT Homework 8 - Solutions
STAT-36700 Homework 8 - Solutions Fall 208 November 3, 208 This contains solutions for Homework 4. lease note that we have included several additional comments and approaches to the problems to give you
5. Series Solutions of ODEs
Advanced Engineering Mathematics 5. Series solutions of ODEs 1 5. Series Solutions of ODEs 5.1 Power series method and Theory of the power series method Advanced Engineering Mathematics 5. Series solutions
GG7: Beyond 2016 FROM PARIS TO ISE-SHIMA. The State of Climate Negotiations: What to Expect after COP 21. g20g7.com
7: By 2016 A B Dy b B R INSIDE 7 ELOME: Sz Ab, P M J EONOMY T Ex EL D Ey D Sy ROM PARIS TO ISE-SHIMA T S N: Ex OP 21 A Pb by AT y I-S S ATOMPANYI Pb T 7 Mz VIP, D, D L 7: By 2016 A B Dy b B R ATOMPANYI
Motion Models (cont) 1 2/15/2012
Motion Models (cont 1 Odometry Motion Model the key to computing p( xt ut, xt 1 for the odometry motion model is to remember that the robot has an internal estimate of its pose θ x t 1 x y θ θ true poses
Math 212-Lecture 8. The chain rule with one independent variable
Math 212-Lecture 8 137: The multivariable chain rule The chain rule with one independent variable w = f(x, y) If the particle is moving along a curve x = x(t), y = y(t), then the values that the particle
Integration - Past Edexcel Exam Questions
Integration - Past Edexcel Exam Questions 1. (a) Given that y = 5x 2 + 7x + 3, find i. - ii. - (b) ( 1 + 3 ) x 1 x dx. [4] 2. Question 2b - January 2005 2. The gradient of the curve C is given by The point
Math 132 Lab 3: Differential Equations
Math 132 Lab 3: Differential Equations Instructions. Follow the directions in each part of the lab. The lab report is due Monday, April 19. You need only hand in these pages. Answer each lab question in
MCV4U - Practice Mastery Test #1
Name: Class: Date: ID: A MCVU - Practice Mastery Test # Multiple Choice Identify the choice that best completes the statement or answers the question.. Solve a + b = a b = 5 a. a= & b=- b. a=- & b= c.
Name: Class: Date: PostAssessment Polynomial Unit. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: _ lass: _ ate: Postssessment Polynomial Unit Multiple hoice Identify the choice that best completes the statement or answers the question. 1 Write the polynomial in standard form. Then name the polynomial
Formalism of Quantum Mechanics
The theory of quantum mechanics is formulated by defining a set of rules or postulates. These postulates cannot be derived from the laws of classical physics. The rules define the following: 1. How to
Midterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.
Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.
PanHomc'r I'rui;* :".>r '.a'' W"»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 >
5 28 (x / &» )»(»»» Q ( 3 Q» (» ( (3 5» ( q 2 5 q 2 5 5 8) 5 2 2 ) ~ ( / x {» /»»»»» (»»» ( 3 ) / & Q ) X ] Q & X X X x» 8 ( &» 2 & % X ) 8 x & X ( #»»q 3 ( ) & X 3 / Q X»»» %» ( z 22 (»» 2» }» / & 2 X
STAD57 Time Series Analysis. Lecture 23
STAD57 Time Series Analysis Lecture 23 1 Spectral Representation Spectral representation of stationary {X t } is: 12 i2t Xt e du 12 1/2 1/2 for U( ) a stochastic process with independent increments du(ω)=
21-256: Partial differentiation
21-256: Partial differentiation Clive Newstead, Thursday 5th June 2014 This is a summary of the important results about partial derivatives and the chain rule that you should know. Partial derivatives
f(x) f(z) c x z > 0 1
INVERSE AND IMPLICIT FUNCTION THEOREMS I use df x for the linear transformation that is the differential of f at x.. INVERSE FUNCTION THEOREM Definition. Suppose S R n is open, a S, and f : S R n is a
Problem set 7 Math 207A, Fall 2011 Solutions
Problem set 7 Math 207A, Fall 2011 s 1. Classify the equilibrium (x, y) = (0, 0) of the system x t = x, y t = y + x 2. Is the equilibrium hyperbolic? Find an equation for the trajectories in (x, y)- phase
JUST THE MATHS UNIT NUMBER ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) A.J.Hobson
JUST THE MATHS UNIT NUMBER 15.3 ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) by A.J.Hobson 15.3.1 Linear equations 15.3.2 Bernouilli s equation 15.3.3 Exercises 15.3.4 Answers to exercises
Chapter 6: Rational Expr., Eq., and Functions Lecture notes Math 1010
Section 6.1: Rational Expressions and Functions Definition of a rational expression Let u and v be polynomials. The algebraic expression u v is a rational expression. The domain of this rational expression
MCR3U - Practice Mastery Test #6
Name: Class: Date: MCRU - Practice Mastery Test #6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Factor completely: 4x 2 2x + 9 a. (2x ) 2 b. (4x )(x )
MAT 419 Lecture Notes Transcribed by Eowyn Cenek 6/1/2012
(Homework 1: Chapter 1: Exercises 1-7, 9, 11, 19, due Monday June 11th See also the course website for lectures, assignments, etc) Note: today s lecture is primarily about definitions Lots of definitions
2.4 The Precise Definition of a Limit
2.4 The Precise Definition of a Limit Reminders/Remarks: x 4 < 3 means that the distance between x and 4 is less than 3. In other words, x lies strictly between 1 and 7. So, x a < δ means that the distance
Strauss PDEs 2e: Section Exercise 1 Page 1 of 6
Strauss PDEs e: Setion.1 - Exerise 1 Page 1 of 6 Exerise 1 Solve u tt = u xx, u(x, 0) = e x, u t (x, 0) = sin x. Solution Solution by Operator Fatorization By fatoring the wave equation and making a substitution,
8-1: Backpropagation Prof. J.C. Kao, UCLA. Backpropagation. Chain rule for the derivatives Backpropagation graphs Examples
8-1: Backpropagation Prof. J.C. Kao, UCLA Backpropagation Chain rule for the derivatives Backpropagation graphs Examples 8-2: Backpropagation Prof. J.C. Kao, UCLA Motivation for backpropagation To do gradient
Optimization Theory. Linear Operators and Adjoints
Optimization Theory Linear Operators and Adjoints A transformation T. : X Y y Linear Operators y T( x), x X, yy is the image of x under T The domain of T on which T can be defined : D X The range of T
b) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true
Section 5.2 solutions #1-10: a) Perform the division using synthetic division. b) if the remainder is 0 use the result to completely factor the dividend (this is the numerator or the polynomial to the
ln(9 4x 5 = ln(75) (4x 5) ln(9) = ln(75) 4x 5 = ln(75) ln(9) ln(75) ln(9) = 1. You don t have to simplify the exact e x + 4e x
Math 11. Exponential and Logarithmic Equations Fall 016 Instructions. Work in groups of 3 to solve the following problems. Turn them in at the end of class for credit. Names. 1. Find the (a) exact solution
Strauss PDEs 2e: Section Exercise 2 Page 1 of 6. Solve the completely inhomogeneous diffusion problem on the half-line
Strauss PDEs 2e: Section 3.3 - Exercise 2 Page of 6 Exercise 2 Solve the completely inhomogeneous diffusion problem on the half-line v t kv xx = f(x, t) for < x
Sect Definitions of a 0 and a n
5 Sect 5. - Definitions of a 0 and a n Concept # Definition of a 0. Let s examine the quotient rule when the powers are equal. Simplify: Ex. 5 5 There are two ways to view this problem. First, any non-zero
There are two basic kinds of random variables continuous and discrete.
Summary of Lectures 5 and 6 Random Variables The random variable is usually represented by an upper case letter, say X. A measured value of the random variable is denoted by the corresponding lower case
' Liberty and Umou Ono and Inseparablo "
3 5? #< q 8 2 / / ) 9 ) 2 ) > < _ / ] > ) 2 ) ) 5 > x > [ < > < ) > _ ] ]? <
MATH 155A FALL 13 PRACTICE MIDTERM 1 SOLUTIONS. needs to be non-zero, thus x 1. Also 1 +
MATH 55A FALL 3 PRACTICE MIDTERM SOLUTIONS Question Find te domain of te following functions (a) f(x) = x3 5 x +x 6 (b) g(x) = x+ + x+ (c) f(x) = 5 x + x 0 (a) We need x + x 6 = (x + 3)(x ) 0 Hence Dom(f)
7.1 Linear Systems Stability Consider the Continuous-Time (CT) Linear Time-Invariant (LTI) system
7 Stability 7.1 Linear Systems Stability Consider the Continuous-Time (CT) Linear Time-Invariant (LTI) system ẋ(t) = A x(t), x(0) = x 0, A R n n, x 0 R n. (14) The origin x = 0 is a globally asymptotically
Tangent Plane. Linear Approximation. The Gradient
Calculus 3 Lia Vas Tangent Plane. Linear Approximation. The Gradient The tangent plane. Let z = f(x, y) be a function of two variables with continuous partial derivatives. Recall that the vectors 1, 0,
Practice Problems for Exam 3 (Solutions) 1. Let F(x, y) = xyi+(y 3x)j, and let C be the curve r(t) = ti+(3t t 2 )j for 0 t 2. Compute F dr.
1. Let F(x, y) xyi+(y 3x)j, and let be the curve r(t) ti+(3t t 2 )j for t 2. ompute F dr. Solution. F dr b a 2 2 F(r(t)) r (t) dt t(3t t 2 ), 3t t 2 3t 1, 3 2t dt t 3 dt 1 2 4 t4 4. 2. Evaluate the line
Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations
Class: Date: Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations 1 Express the following polynomial function in factored form: P( x) = 10x 3 + x 2 52x + 20 2 SE: Express the following
In-Class Problems 20-21: Work and Kinetic Energy Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 In-Class Problems 20-21: Work and Kinetic Energy Solutions In-Class-Problem 20 Calculating Work Integrals a) Work
T T - PTV - PTV :\er\en utler.p\ektop\ VT \9- T\_ T.rvt T PT P ode aterial. Pattern / olor imenion omment PT T T ode aterial. Pattern / olor imenion omment W T ode aterial. Pattern / olor imenion omment
Unit 3 Factors & Products
1 Unit 3 Factors & Products General Outcome: Develop algebraic reasoning and number sense. Specific Outcomes: 3.1 Demonstrate an understanding of factors of whole number by determining the: o prime factors
Solving and Graphing Inequalities Joined by And or Or
Solving and Graphing Inequalities Joined by And or Or Classwork 1. Zara solved the inequality 18 < 3x 9 as shown below. Was she correct? 18 < 3x 9 27 < 3x 9 < x or x> 9 2. Consider the compound inequality
Nonlinear Programming
Nonlinear Programming Kees Roos e-mail: C.Roos@ewi.tudelft.nl URL: http://www.isa.ewi.tudelft.nl/ roos LNMB Course De Uithof, Utrecht February 6 - May 8, A.D. 2006 Optimization Group 1 Outline for week
Learning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.
Learning Target: I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 3x 3 (x+2) 2 a. Determine the equation(s) of the asymptotes. b. Find the
5 Operations on Multiple Random Variables
EE360 Random Signal analysis Chapter 5: Operations on Multiple Random Variables 5 Operations on Multiple Random Variables Expected value of a function of r.v. s Two r.v. s: ḡ = E[g(X, Y )] = g(x, y)f X,Y
Proc. of the 23rd Intl. Conf. on Parallel Processing, St. Charles, Illinois, August 1994, vol. 3, pp. 227{ Hanan Samet
P. 23 Il. C. Plll P, S. Cl, Ill, 1994, vl. 3,. 227{234 1 DT-PRE SPTI JOI GORITHMS Ek G. Hl y Gy Dv B C W, D.C. 20233 H S C S D C R I v C S Uvy Myl Cll Pk, Myl 20742 { E -lll l j l R-, l,. T l l (.., B
ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS
ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS RBFN and TS systems Equivalent if the following hold: Both RBFN and TS use same aggregation method for output (weighted sum or weighted average) Number of basis functions
LOWELL WEEKLY JOURNAL.
Y 5 ; ) : Y 3 7 22 2 F $ 7 2 F Q 3 q q 6 2 3 6 2 5 25 2 2 3 $2 25: 75 5 $6 Y q 7 Y Y # \ x Y : { Y Y Y : ( \ _ Y ( ( Y F [ F F ; x Y : ( : G ( ; ( ~ x F G Y ; \ Q ) ( F \ Q / F F \ Y () ( \ G Y ( ) \F
Advanced Radiology Reporting and Analytics with rscriptor vrad results after 10 million radiology reports
Av Ry R Ay wh vr 10 y I, w, v, - y y h, v, z yz y. I wh vy y v y hh-qy y z. A h h h N L P (NLP) h w y y. h w w vr Jy 2014 h h h 10 y. F h - w vr hv wk h v h qy wkw. h wh h h. I I /v h h wk wh vy y v w
Math 222 Spring 2013 Exam 3 Review Problem Answers
. (a) By the Chain ule, Math Spring 3 Exam 3 eview Problem Answers w s w x x s + w y y s (y xy)() + (xy x )( ) (( s + 4t) (s 3t)( s + 4t)) ((s 3t)( s + 4t) (s 3t) ) 8s 94st + 3t (b) By the Chain ule, w
Math 226 Calculus Spring 2016 Practice Exam 1. (1) (10 Points) Let the differentiable function y = f(x) have inverse function x = f 1 (y).
Math 6 Calculus Spring 016 Practice Exam 1 1) 10 Points) Let the differentiable function y = fx) have inverse function x = f 1 y). a) Write down the formula relating the derivatives f x) and f 1 ) y).
Chapter 7: Exponents
Chapter : Exponents Algebra Chapter Notes Name: Notes #: Sections.. Section.: Review Simplify; leave all answers in positive exponents:.) m -.) y -.) m 0.) -.) -.) - -.) (m ) 0.) 0 x y Evaluate if a =
LESSON 23: EXTREMA OF FUNCTIONS OF 2 VARIABLES OCTOBER 25, 2017
LESSON : EXTREMA OF FUNCTIONS OF VARIABLES OCTOBER 5, 017 Just like with functions of a single variable, we want to find the minima (plural of minimum) and maxima (plural of maximum) of functions of several
PDEs, Homework #3 Solutions. 1. Use Hölder s inequality to show that the solution of the heat equation
PDEs, Homework #3 Solutions. Use Hölder s inequality to show that the solution of the heat equation u t = ku xx, u(x, = φ(x (HE goes to zero as t, if φ is continuous and bounded with φ L p for some p.
E A S Y & E F F E C T I V E S K I N S O L U T I O N S
E A S Y & E F F E C T I V E S K I N S O L U T I O N S EASY & EFFECTIVE SKIN SOLUTIONS D ñ í q, á bj ó í; é, b ó. E q b, q ó q. N b b, á, q q,, ó ó á b. Aí PUREDERM, ñí bó á. P "H C", á 15 ñ x ó é. Uz á
Linearized Equations of Motion!
Linearized Equations of Motion Robert Stengel, Aircraft Flight Dynamics MAE 331, 216 Learning Objectives Develop linear equations to describe small perturbational motions Apply to aircraft dynamic equations