IFYFM002 Further Maths Appendix C Formula Booklet
|
|
|
- Tracy Cain
- 5 years ago
- Views:
Transcription
1 Ittol Foudto Y (IFY) IFYFM00 Futh Mths Appd C Fomul Booklt Rltd Documts: IFY Futh Mthmtcs Syllbus 07/8
2 Cotts Mthmtcs Fomul L Equtos d Mtcs... Qudtc Equtos d Rmd Thom... Boml Epsos, Squcs d Ss... Idcs, Epotl d Logthmc Fuctos... Tgoomtc Fuctos d Idtts... Dtto...4 Itgto...5 Vctos...6 Numcl mthods...6 Itoducto to Sttstcs...7 Futh Mthmtcs Fomul Pls ot tht th ltts gv th hdg o ch scto to th topc o th syllbus to whch th omul lt. A & L - Compl Numbs...8 B - Mtcs...8 D & J - Ss...9 G - Hypbolc Fuctos... 0 I - Coc Sctos... 0 M - Futh Dtto d Itgto... N - Vctos... Sttstcl Tbls Noml Dstbuto Tbl... Tl Pobblty P... 4
3 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Mthmtcs Fomul L Equtos d Mtcs Stght L y m c, wh m s th slop o gdt, d c s th y -tcpt L though pots 0, y 0, y d y y 0 0 y y 0 0 Ivs o mt I b d b A, th A c d d bc c d bc Qudtc Equtos d Rmd Thom Qudtc Fomul I b c 0, th b b 4c 0 07 Noth Cosotum UK Ltd. Pg o 4
4 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Boml Epsos, Squcs d Ss Boml Ss Wh s postv tg, ( b) b b... b b ( b) 0 b C!!( )! Wh s ot postv tg ( ) ( )( ) ( )...,!! Athmtc Ss (AP) s th st tm, d s th commo dc th tm: u ( ) d, Sum to tms: S ( ( ) d) Gomtc Ss (GP) povdd, R. s th st tm, s th commo to th tm: u Sum to tms: S ( ) Sum to ty: S, povdd 07 Noth Cosotum UK Ltd. Pg o 4
5 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Idcs, Epotl d Logthmc Fuctos log log log b b l Tgoomtc Fuctos d Idtts s cos b c bc cos A s A s B b s C c Doubl gl: s s cos cos cos s s cos Sums d dcs: s( A B) s Acos B cos As B cos( A B) cos Acos B s As B t A t B t( A B) t At B 07 Noth Cosotum UK Ltd. Pg o 4
6 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Dtto () k l s cos t d ( ) d ( ) ( ) () ( ) d d sc sc t k k csc csc cot cot csc cos s s cos sc t Ch Rul: I y s ucto o u d u s ucto o, th dy d dy du. du d Poduct Rul: I y uv, wh u d v uctos o, th dy d du dv v u d d Quott Rul: I u y v wh u d v uctos o, th du dv v u dy d d d v 07 Noth Cosotum UK Ltd. Pg 4 o 4
7 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Itgto (), l l b s cos cos t ( ) d () b sc csc cot s l cos ( ) d l sc t l csc cot l s s, t Itgto by pts dv u d uv d Applctos o tgto du v d d A ud cuv: Volum o voluto: A b y d b V y d 07 Noth Cosotum UK Ltd. Pg 5 o 4
8 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Vctos Ut vcto â th dcto o ˆ, wh s th modulus (mgtud) o. Scl Poduct. b b cos wh s th gl btw d b.. b b. I j k d b b b j b k, wh, j d k ut vctos th, y d z dctos, th. j.j k.k,. j jk. k. 0,.b, b b b.. I both d b o-zo vctos th s ppdcul to b.b 0. Numcl mthods Soluto o ( ) 0 gv 0, Nwto-Rphso: ( ) ( ) 0,,, 07 Noth Cosotum UK Ltd. Pg 6 o 4
9 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt 07 Noth Cosotum UK Ltd. Pg 7 o 4 Itoducto to Sttstcs Msus o vg d spd Ugoupd Dt Goupd Dt M Vc Stdd Dvto Chg o og/scl : I ) ( k X, th ) ( k X X k.
10 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Futh Mthmtcs Fomul A & L - Compl Numbs z y cos s cos s wh cos s Th oots o z gv by k z o k 0,,,,. Th symbol j s lso usd to dot B - Mtcs L tsomtos Rlcto bout th - s: 0 0 Rlcto bout th y- s: 0 0 Rlcto bout th l y = : 0 0 Atclockws otto though gl bout th og: cos s s cos Ivs o mt d g b h c A D G B E H C F I T, wh d g b h c 07 Noth Cosotum UK Ltd. Pg 8 o 4
11 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt D & J - Ss Mclu Ss 6 4 ( ) Gl ss: ( ) (0) (0) (0)... (0)...!!!...!..., o ll l( )... ( ), s! 5 5!... ( )..., ( )! o ll 4 cos... ( )! 4!..., ()! o ll ct 5 5, Tylo ss 5 sh......,! 5! ( )! 4 cosh......,! 4! ()! o ll o ll!! o!! 07 Noth Cosotum UK Ltd. Pg 9 o 4
12 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt G - Hypbolc Fuctos cosh sh cosh sh sh sh cosh, cosh cosh sh sh l( ) cosh l( ), th l, I - Coc Sctos Cts Fom Pmtc Fom Ecctcty Foc,0 Pbol Ellps Rctgul Hypbol y 4 y y c b ( t,) t ( cos, bs) c ct, t (,0 ) ( c, c ) Dct Dctcs Asymptots 0, y 0 07 Noth Cosotum UK Ltd. Pg 0 o 4
13 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt M - Futh Dtto d Itgto Dtto () d ( ) ( ) d sh cosh cosh sh th sch sh cosh th Itgto () sh cosh th ( ) d cosh sh l cosh sh cosh, th Ac lgth: L Suc o voluto wh th c th -s: dy d d d dt dy dt dt y s ottd though ds bout S y ds y dy d y d d dt dy dt dt 07 Noth Cosotum UK Ltd. Pg o 4
14 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt N - Vctos Vcto Poduct b b s, wh s th gl btw d b, ppdcul to both d b. d s ut vcto b b I j k d b b b j b k, wh, j d k ut vctos th, y d z dctos, th j j k k 0, j k, jk, k j, b b b ) ( b b ) j ( b ) k. ( b I both d b o-zo vctos th s plll to b b Noth Cosotum UK Ltd. Pg o 4
15 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Noml Dstbuto Tbl I Z hs oml dstbuto wth m = 0 d vc =, th tbl gvs th pobblty, p tht Z s lss th o qul to z. z Noth Cosotum UK Ltd. Pg o 4
16 IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Tl Pobblty P Dg o Fdom Noth Cosotum UK Ltd. Pg 4 o 4
CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.
CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.
GCE AS/A Level MATHEMATICS GCE AS/A Level FURTHER MATHEMATICS
GCE AS/A Level MATHEMATICS GCE AS/A Level FURTHER MATHEMATICS FORMULA BOOKLET Fom Septembe 07 Issued 07 Mesuto Pue Mthemtcs Sufce e of sphee = 4 Ae of cuved sufce of coe = slt heght Athmetc Sees S l d
CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find
BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,
Chapter 2 Reciprocal Lattice. An important concept for analyzing periodic structures
Chpt Rcpocl Lttc A mpott cocpt o lyzg podc stuctus Rsos o toducg cpocl lttc Thoy o cystl dcto o x-ys, utos, d lctos. Wh th dcto mxmum? Wht s th tsty? Abstct study o uctos wth th podcty o Bvs lttc Fou tsomto.
New Advanced Higher Mathematics: Formulae
Advcd High Mthmtics Nw Advcd High Mthmtics: Fomul G (G): Fomul you must mmois i od to pss Advcd High mths s thy ot o th fomul sht. Am (A): Ths fomul giv o th fomul sht. ut it will still usful fo you to
GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd.
GCE AS d A Level MATHEMATICS FORMULA BOOKLET Fom Septeme 07 Issued 07 Pue Mthemtcs Mesuto Suce e o sphee = 4 Ae o cuved suce o coe = heght slt Athmetc Sees S = + l = [ + d] Geometc Sees S = S = o < Summtos
The formulae in this booklet have been arranged according to the unit in which they are first
Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge ccog to the ut whch the e fst touce. Thus cte sttg ut m e eque to use the fomule tht wee touce peceg ut e.g. ctes sttg C mght e epecte to use
PhysicsAndMathsTutor.com
PhysicsAdMthsTuto.com 5. () Show tht d y d PhysicsAdMthsTuto.com Jue 009 4 y = sec = 6sec 4sec. (b) Fid Tylo seies epsio of sec π i scedig powes of 4, up to d 3 π icludig the tem i 4. (6) (4) blk *M3544A08*
The formulae in this booklet have been arranged according to the unit in which they are first
Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule
Handout 7. Properties of Bloch States and Electron Statistics in Energy Bands
Hdout 7 Popts of Bloch Stts d Elcto Sttstcs Eg Bds I ths lctu ou wll l: Popts of Bloch fuctos Podc boud codtos fo Bloch fuctos Dst of stts -spc Elcto occupto sttstcs g bds ECE 407 Spg 009 Fh R Coll Uvst
PhysicsAndMathsTutor.com
PhysicsAdMthsTuto.com PhysicsAdMthsTuto.com Jue 009 3. Fid the geel solutio of the diffeetil equtio blk d si y ycos si si, d givig you swe i the fom y = f(). (8) 6 *M3544A068* PhysicsAdMthsTuto.com Jue
Order Statistics from Exponentiated Gamma. Distribution and Associated Inference
It J otm Mth Scc Vo 4 9 o 7-9 Od Stttc fom Eottd Gmm Dtto d Aoctd Ifc A I Shw * d R A Bo G og of Edcto PO Bo 369 Jddh 438 Sd A G og of Edcto Dtmt of mthmtc PO Bo 469 Jddh 49 Sd A Atct Od tttc fom ottd
COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES
COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES DEFINITION OF A COMPLEX NUMBER: A umbr of th form, whr = (, ad & ar ral umbrs s calld a compl umbr Th ral umbr, s calld ral part of whl s calld
Advanced Higher Maths: Formulae
: Fomule Gee (G): Fomule you bsolutely must memoise i ode to pss Advced Highe mths. Remembe you get o fomul sheet t ll i the em! Ambe (A): You do t hve to memoise these fomule, s it is possible to deive
Section 5.1/5.2: Areas and Distances the Definite Integral
Scto./.: Ars d Dstcs th Dt Itgrl Sgm Notto Prctc HW rom Stwrt Ttook ot to hd p. #,, 9 p. 6 #,, 9- odd, - odd Th sum o trms,,, s wrtt s, whr th d o summto Empl : Fd th sum. Soluto: Th Dt Itgrl Suppos w
For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations
GCE Edecel GCE Mthemtcs Mthemtcl Fomule d Sttstcl Tles Fo use Edecel Advced Susd GCE d Advced GCE emtos Coe Mthemtcs C C4 Futhe Pue Mthemtcs FP FP Mechcs M M5 Sttstcs S S4 Fo use fom Ju 008 UA08598 TABLE
PhysicsAndMathsTutor.com
PhysicsAdMthsTuto.com PhysicsAdMthsTuto.com Jue 009 7. () Sketch the gph of y, whee >, showig the coodites of the poits whee the gph meets the es. () Leve lk () Solve, >. (c) Fid the set of vlues of fo
Inner Product Spaces INNER PRODUCTS
MA4Hcdoc Ir Product Spcs INNER PRODCS Dto A r product o vctor spc V s ucto tht ssgs ubr spc V such wy tht th ollowg xos holds: P : w s rl ubr P : P : P 4 : P 5 : v, w = w, v v + w, u = u + w, u rv, w =
IFYMB002 Mathematics Business Appendix C Formula Booklet
Iteratoal Foudato Year (IFY IFYMB00 Mathematcs Busess Apped C Formula Booklet Related Documet: IFY Mathematcs Busess Syllabus 07/8 IFYMB00 Maths Busess Apped C Formula Booklet Cotets lease ote that the
Chapter Linear Regression
Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use
National Quali cations
PRINT COPY OF BRAILLE Ntiol Quli ctios AH08 X747/77/ Mthmtics THURSDAY, MAY INSTRUCTIONS TO CANDIDATES Cdidts should tr thir surm, form(s), dt of birth, Scottish cdidt umbr d th m d Lvl of th subjct t
PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Basic Science and Humanities
P E PESIT Bglo South Cpus Hosu od, k bfo Elctoic Cit, Bgluu -00 Dptt of Bsic Scic d Huitis INTERNAL ASSESSMENT TEST Dt : 0/0/07 Mks: 0 Subjct & Cod : Egiig Mthtics I 5MAT Sc : ALL N of fcult : GVR,GKJ,RR,SV,NHM,DN,KR,
National Quali cations
Ntiol Quli ctios AH07 X77/77/ Mthmtics FRIDAY, 5 MAY 9:00 AM :00 NOON Totl mrks 00 Attmpt ALL qustios. You my us clcultor. Full crdit will b giv oly to solutios which coti pproprit workig. Stt th uits
Path (space curve) Osculating plane
Fo th cuilin motion of pticl in spc th fomuls did fo pln cuilin motion still lid. But th my b n infinit numb of nomls fo tngnt dwn to spc cu. Whn th t nd t ' unit ctos mod to sm oigin by kping thi ointtions
AS and A Level Further Mathematics B (MEI)
fod Cmbdge d RSA *3369600* AS d A evel Futhe Mthemtcs B (MEI) The fomto ths booklet s fo the use of cddtes followg the Advced Subsd Futhe Mthemtcs B (MEI)(H635) o the Advced GCE Futhe Mthemtcs B (MEI)
Boyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues
BocDPm 9 h d Ch 7.6: Compl Egvlus Elm Dffl Equos d Boud Vlu Poblms 9 h do b Wllm E. Boc d Rchd C. DPm 9 b Joh Wl & Sos Ic. W cosd g homogous ssm of fs od l quos wh cos l coffcs d hus h ssm c b w s ' A
Advanced Higher Maths: Formulae
Advced Highe Mths: Fomule Advced Highe Mthemtics Gee (G): Fomule you solutely must memoise i ode to pss Advced Highe mths. Rememe you get o fomul sheet t ll i the em! Ame (A): You do t hve to memoise these
ERDOS-SMARANDACHE NUMBERS. Sabin Tabirca* Tatiana Tabirca**
ERDO-MARANDACHE NUMBER b Tbrc* Tt Tbrc** *Trslv Uvrsty of Brsov, Computr cc Dprtmt **Uvrsty of Mchstr, Computr cc Dprtmt Th strtg pot of ths rtcl s rprstd by rct work of Fch []. Bsd o two symptotc rsults
Mathematics HL and further mathematics HL formula booklet
Dplom Progrmme Mthemtcs HL d further mthemtcs HL formul boolet For use durg the course d the emtos Frst emtos 04 Publshed Jue 0 Itertol Bcclurete Orgzto 0 5048 Cotets Pror lerg Core Topc : Algebr Topc
Convergence tests for the cluster DFT calculations
Covgc ss o h clus DF clculos. Covgc wh spc o bss s. s clculos o bss s covgc hv b po usg h PBE ucol o 7 os gg h-b. A s o h Guss bss ss wh csg s usss hs b us clug h -G -G** - ++G(p). A l sc o. Å h c bw h
COMPLEX NUMBERS AND DE MOIVRE S THEOREM
COMPLEX NUMBERS AND DE MOIVRE S THEOREM OBJECTIVE PROBLEMS. s equl to b d. 9 9 b 9 9 d. The mgr prt of s 5 5 b 5. If m, the the lest tegrl vlue of m s b 8 5. The vlue of 5... s f s eve, f s odd b f s eve,
Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates.
CURVE FITTING Descbes techques to ft cuves (cuve fttg) to dscete dt to obt temedte estmtes. Thee e two geel ppoches fo cuve fttg: Regesso: Dt ehbt sgfct degee of sctte. The stteg s to deve sgle cuve tht
Surface x(u, v) and curve α(t) on it given by u(t) & v(t). Math 4140/5530: Differential Geometry
Surface x(u, v) and curve α(t) on it given by u(t) & v(t). α du dv (t) x u dt + x v dt Surface x(u, v) and curve α(t) on it given by u(t) & v(t). α du dv (t) x u dt + x v dt ( ds dt )2 Surface x(u, v)
ME 501A Seminar in Engineering Analysis Page 1
Mtr Trsformtos usg Egevectors September 8, Mtr Trsformtos Usg Egevectors Lrry Cretto Mechcl Egeerg A Semr Egeerg Alyss September 8, Outle Revew lst lecture Trsformtos wth mtr of egevectors: = - A ermt
D. Bertsekas and R. Gallager, "Data networks." Q: What are the labels for the x-axis and y-axis of Fig. 4.2?
pd by J. Succ ECE 543 Octob 22 2002 Outl Slottd Aloh Dft Stblzd Slottd Aloh Uslottd Aloh Splttg Algoths Rfc D. Btsks d R. llg "Dt twoks." Rvw (Slottd Aloh): : Wht th lbls fo th x-xs d y-xs of Fg. 4.2?
SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE
D I D A C T I C S O F A T H E A T I C S No (4) 3 SOE REARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOIAL ASYPTOTE Tdeusz Jszk Abstct I the techg o clculus, we cosde hozotl d slt symptote I ths ppe the
Chapter 17. Least Square Regression
The Islmc Uvest of Gz Fcult of Egeeg Cvl Egeeg Deptmet Numecl Alss ECIV 336 Chpte 7 Lest que Regesso Assocte Pof. Mze Abultef Cvl Egeeg Deptmet, The Islmc Uvest of Gz Pt 5 - CURVE FITTING Descbes techques
PhysicsAndMathsTutor.com
PhysicsAMthsTuto.com . M 6 0 7 0 Leve lk 6 () Show tht 7 is eigevlue of the mti M fi the othe two eigevlues of M. (5) () Fi eigevecto coespoig to the eigevlue 7. *M545A068* (4) Questio cotiue Leve lk *M545A078*
Statics. Consider the free body diagram of link i, which is connected to link i-1 and link i+1 by joint i and joint i-1, respectively. = r r r.
Statcs Th cotact btw a mapulato ad ts vomt sults tactv ocs ad momts at th mapulato/vomt tac. Statcs ams at aalyzg th latoshp btw th actuato dv tous ad th sultat oc ad momt appld at th mapulato dpot wh
Exponentiated Weibull-Exponential Distribution with Applications
Avlbl t http://pvmudu/m Appl Appl Mth ISSN: 93-9466 Vol, Issu (Dcmb 07), pp 70-75 Applctos d Appld Mthmtcs: A Ittol Joul (AAM) Epottd Wbull-Epotl Dstbuto wth Applctos M Elghy, M Shkl d BM Golm Kb 3 Abstct
Mathematics HL and further mathematics HL formula booklet
Dplom Progrmme Mthemtcs HL d further mthemtcs HL formul boolet For use durg the course d the emtos Frst emtos 04 Publshed Jue 0 Itertol Bcclurete Orgzto 0 5048 Mthemtcs HL d further mthemtcs formul boolet
Mathematics HL and further mathematics HL formula booklet
Dplom Progrmme Mthemtcs HL d further mthemtcs HL formul boolet For use durg the course d the emtos Frst emtos 04 Edted 05 (verso ) Itertol Bcclurete Orgzto 0 5048 Cotets Pror lerg Core 3 Topc : Algebr
WELSH JOINT EDUCATION COMMITTEE CYD-BWYLLGOR ADDYSG CYMRU MATHEMATICS. FORMULA BOOKLET (New Specification)
WELSH JOINT EDUCATION COMMITTEE CYD-BWYLLGOR ADDYSG CYMRU Gl Ciic o Eucio Avc Lvl/Avc Susii Tssgi Asg Giol So Uwch/Uwch Gol MATHEMATICS FORMULA BOOKLET Nw Spciicio Issu 004 Msuio Suc o sph 4π A o cuv suc
SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy.
LTNY OF TH SNTS Cntrs Gnt flwng ( = c. 100) /G Ddd9/F ll Kybrd / hv Ddd9 hv hv Txt 1973, CL. ll rghts rsrvd. Usd wth prmssn. Musc: D. Bckr, b. 1953, 1987, D. Bckr. Publshd by OCP. ll rghts rsrvd. SMPL
GUC (Dr. Hany Hammad)
Lct # Pl s. Li bdsid s with ifm mplitd distibtis. Gl Csidtis Uifm Bimil Optimm (Dlph-Tchbshff) Cicl s. Pl s ssmig ifm mplitd citti m F m d cs z F d d M COMM Lct # Pl s ssmig ifm mplitd citti F m m m T
FOURIER SERIES. Series expansions are a ubiquitous tool of science and engineering. The kinds of
Do Bgyoko () FOURIER SERIES I. INTRODUCTION Srs psos r ubqutous too o scc d grg. Th kds o pso to utz dpd o () th proprts o th uctos to b studd d (b) th proprts or chrctrstcs o th systm udr vstgto. Powr
SOLVED EXAMPLES. Ex.1 If f(x) = , then. is equal to- Ex.5. f(x) equals - (A) 2 (B) 1/2 (C) 0 (D) 1 (A) 1 (B) 2. (D) Does not exist = [2(1 h)+1]= 3
![SOLVED EXAMPLES. Ex.1 If f(x) = , then. is equal to- Ex.5. f(x) equals - (A) 2 (B) 1/2 (C) 0 (D) 1 (A) 1 (B) 2. (D) Does not exist = [2(1 h)+1]= 3](/thumbs/89/98215718.jpg "SOLVED EXAMPLES. Ex.1 If f(x) = , then. is equal to- Ex.5. f(x) equals - (A) 2 (B) 1/2 (C) 0 (D) 1 (A) 1 (B) 2. (D) Does not exist = [2(1 h)+1]= 3")
SOLVED EXAMPLES E. If f() E.,,, th f() f() h h LHL RHL, so / / Lim f() quls - (D) Dos ot ist [( h)+] [(+h) + ] f(). LHL E. RHL h h h / h / h / h / h / h / h As.[C] (D) Dos ot ist LHL RHL, so giv it dos
PhysicsAndMathsTutor.com
PhsicsAMthsTuto.com 6. The hpeol H hs equtio, whee e costts. The lie L hs equtio m c, whee m c e costts. Leve lk () Give tht L H meet, show tht the -cooites of the poits of itesectio e the oots of the
ATTACHMENT 1. MOUNTAIN PARK LAND Page 2 of 5
ATTACHMENT 53 YOBA LINDA Gyp Yb gl 9 Gt Fthly gl t 247 Mt Utct cl Mt Gyp 248 248X A0 A0 Hghy G:\jct\K00074232_p_Iv_Cp_L_Dt_204\MXD\p_Iv_Cp_L_Dt_(K00074232)_0-29-204.x C ( l t b t f y p b lc ly ) Ch Hll
2sin cos dx. 2sin sin dx
Fou S & Fou To Th udtl d tht y podc ucto (.. o tht pt t ptcul tvl) c b pd t u o d co wv o dt pltud d qucy. Th c b glzd to tgl (Th Fou To), whch h wd gg pplcto o th oluto o dtl quto whch occu th Phycl cc.
COLLECTION OF SUPPLEMENTARY PROBLEMS CALCULUS II
COLLECTION OF SUPPLEMENTARY PROBLEMS I. CHAPTER 6 --- Trscdtl Fuctios CALCULUS II A. FROM CALCULUS BY J. STEWART:. ( How is th umbr dfid? ( Wht is pproimt vlu for? (c ) Sktch th grph of th turl potil fuctios.
A Series Illustrating Innovative Forms of the Organization & Exposition of Mathematics by Walter Gottschalk
The Sgm Summto Notto #8 of Gottschlk's Gestlts A Seres Illustrtg Iovtve Forms of the Orgzto & Exposto of Mthemtcs by Wlter Gottschlk Ifte Vsts Press PVD RI 00 GG8- (8) 00 Wlter Gottschlk 500 Agell St #44
ALPHABET. 0Letter Practice
ALPHABET 0Ltt Pat Ltt Pat - Aa A A A A a a a Cl A s A a a A A Cl a s A a k Aa a Cut ut th ltt s a glu thm th ght st. Catal A Las a 2014 Lau Thms.msthmsstasus.m a a A a A A Ltt Pat - B B B B B Cl B s m
( ) ( ) ( ) 2011 HSC Mathematics Solutions ( 6) ( ) ( ) ( ) π π. αβ = = 2. α β αβ. Question 1. (iii) 1 1 β + (a) (4 sig. fig.
HS Mathmatics Solutios Qustio.778.78 ( sig. fig.) (b) (c) ( )( + ) + + + + d d (d) l ( ) () 8 6 (f) + + + + ( ) ( ) (iii) β + + α α β αβ 6 (b) si π si π π π +,π π π, (c) y + dy + d 8+ At : y + (,) dy 8(
February 12 th December 2018
208 Fbu 2 th Dcb 208 Whgt Fbu Mch M 2* 3 30 Ju Jul Sptb 4* 5 7 9 Octob Novb Dcb 22* 23 Put ou blu bgs out v d. *Collctios d lt du to Public Holid withi tht wk. Rcclig wk is pik Rcclig wk 2 is blu Th stick
to Highbury via Massey University, Constellation Station, Smales Farm Station, Akoranga Station and Northcote
b v Nc, g, F, C Uv Hgb p (p 4030) F g (p 4063) F (p 3353) L D (p 3848) 6.00 6.0 6.2 6.20 6.30 6.45 6.50 6.30 6.40 6.42 6.50 7.00 7.5 7.20 7.00 7.0 7.2 7.20 7.30 7.45 7.50 7.30 7.40 7.42 7.50 8.00 8.5 8.20
MULTI-PRODUCT INVENTORY CONTROL MODEL WITH CONSTRAINTS
spot d lcommucto Vol.7, No, 6 MUIRDU INVNRY NR MD WIH NSRAINS ug Kopytov, Fdo ss, od Gglz spot d lcommucto Isttut omoosov St., Rg, V9, tv h: 37 759. Fx: 37 766. ml: optov@ts.lv, fdotss@ts.lv Rg Ittol School
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
Das Klassik & Jazz Magazin. Mediapack 2018
Ds Kssk & Jzz Mgz Mdpck 2018 Ds Kssk & Jzz Mgz t gc TOPICS RONDO s d by 100% fcds f cssc musc Sc 1992 RONDO s dpy tgtd cutu f RONDO chs th w-fudd tgt udc f cssc musc: gu vsts f ccts d ps, stdy buys f cssc
Handout 11. Energy Bands in Graphene: Tight Binding and the Nearly Free Electron Approach
Hdout rg ds Grh: Tght dg d th Nrl Fr ltro roh I ths ltur ou wll lr: rg Th tght bdg thod (otd ) Th -bds grh FZ C 407 Srg 009 Frh R Corll Uvrst Grh d Crbo Notubs: ss Grh s two dsol sgl to lr o rbo tos rrgd
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
Peso Edecel Level 3 Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
Peso Edecel Level Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics
Sequences and summations
Lecture 0 Sequeces d summtos Istructor: Kgl Km CSE) E-ml: kkm0@kokuk.c.kr Tel. : 0-0-9 Room : New Mleum Bldg. 0 Lb : New Egeerg Bldg. 0 All sldes re bsed o CS Dscrete Mthemtcs for Computer Scece course
OPTICAL DESIGN. FIES fibre assemblies B and C. of the. LENS-TECH AB Bo Lindberg Document name: Optical_documentation_FIES_fiber_BC_2
OPTICAL DESIGN f h FIES fb ssmbs B d C LENS-TECH AB B Ldbg 2-4-3 Dcm m: Opc_dcm_FIES_fb_BC_2 Idc Ths p s dcm f h pc dsg f h FIES fb ssmbs B d C Th mchc dsg s shw I s shw h ssmb dwg md b Ahs Uvs Fb c Th
Quantum Circuits. School on Quantum Day 1, Lesson 5 16:00-17:00, March 22, 2005 Eisuke Abe
Qutum Crcuts School o Qutum Computg @Ygm D, Lsso 5 6:-7:, Mrch, 5 Esuk Ab Dprtmt of Appl Phscs Phsco-Iformtcs, CEST-JST, Ko vrst Outl Bloch sphr rprstto otto gts vrslt proof A rbtrr cotroll- gt c b mplmt
A NEW GENERALIZATION OF THE EXPONENTIAL-GEOMETRIC DISTRIBUTION
Jou of Sttstcs: Advcs Thoy d Actos Voum 7 Num Pgs 5-48 A NW GNRAIZATION OF TH PONNTIA-GOMTRIC DISTRIBUTION M. NASSAR d N. NADA Dtmt of Mthmtcs Fcuty of Scc A Shms Uvsty Ass Co 566 gyt -m: m_ss_999@yhoo.com
Cartesian Coordinate System and Vectors
Catesian Coodinate System and Vectos Coodinate System Coodinate system: used to descibe the position of a point in space and consists of 1. An oigin as the efeence point 2. A set of coodinate axes with
TUESDAY JULY Concerning an Upcoming Change Order for the Clearwell Project. Pages 28 SALLISAW MUNICIPAL AUTHORITY SPECIAL MEETING
SSW MUCP UTHOT SPEC MEETG TUESD U 2 200 0 00M SSW WTE TETMET PT COEECE OOM EPPE OD GED Mg Cd T Od 2 Dc Quum 3 c B P m B P h H W Eg Ccg Upcmg Chg Od h C Pjc Cd d Cc d Ep Ph Pjc Pg 28 dju Pd u 22 200 Tm
o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco
> p >>>> ft^. 2 Tble f Generl rdnes. t^-t - +«0 -P k*ph? -- i t t i S i-h l -H i-h -d. *- e Stf H2 t s - ^ d - 'Ct? "fi p= + V t r & ^ C d Si d n. M. s - W ^ m» H ft ^.2. S'Sll-pl e Cl h /~v S s, -P s'l
ASSERTION AND REASON
ASSERTION AND REASON Som qustios (Assrtio Rso typ) r giv low. Ech qustio cotis Sttmt (Assrtio) d Sttmt (Rso). Ech qustio hs choics (A), (B), (C) d (D) out of which ONLY ONE is corrct. So slct th corrct
3.4 Properties of the Stress Tensor
cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato
660 Chapter 10 Conic Sections and Polar Coordinates
Chpter Conic Sections nd Polr Coordintes 8. ( (b (c (d (e r r Ê r ; therefore cos Ê Ê ( ß is point of intersection ˆ ˆ Ê Ê Ê ß ß ˆ ß 9. ( r cos Ê cos ; r cos Ê r Š Ê r r Ê (r (b r Ê cos Ê cos Ê, Ê ß or
EQUATIONS FOR ALLUVIAL SOIL STORAGE COEFFICIENTS
vomtl gg d gmt Joul Novmb/Dcmb 8, Vol.7, No.6, 89-83 http://omco.ch.tu.o/j/ Ghogh Ach Tchcl Uvty of I, Rom QUATION FOR ALLUVIAL OIL TORAG COFFICINT mld Chocu, Ştf Popcu, Dl Tom Agoomc Uvty of I, Pdologcl
minimize c'x subject to subject to subject to
z ' sut to ' M ' M N uostrd N z ' sut to ' z ' sut to ' sl vrls vtor of : vrls surplus vtor of : uostrd s s s s s s z sut to whr : ut ost of :out of : out of ( ' gr of h food ( utrt : rqurt for h utrt
Get Funky this Christmas Season with the Crew from Chunky Custard
Hol Gd Chcllo Adld o Hdly Fdy d Sudy Nhs Novb Dcb 2010 7p 11.30p G Fuky hs Chss Sso wh h Cw fo Chuky Cusd Fdy Nhs $99pp Sudy Nhs $115pp Tck pc cluds: Full Chss d buff, 4.5 hou bv pck, o sop. Ts & Codos
School of Aerospace Engineering Origins of Quantum Theory. Measurements of emission of light (EM radiation) from (H) atoms found discrete lines
Ogs of Quatu Thoy Masuts of sso of lght (EM adato) fo (H) atos foud dsct ls 5 4 Abl to ft to followg ss psso ν R λ c λwavlgth, νfqucy, cspd lght RRydbg Costat (~09,7677.58c - ),,, +, +,..g.,,.6, 0.6, (Lya
12 Iterative Methods. Linear Systems: Gauss-Seidel Nonlinear Systems Case Study: Chemical Reactions
HK Km Slghtly moded //9 /8/6 Frstly wrtte t Mrch 5 Itertve Methods er Systems: Guss-Sedel Noler Systems Cse Study: Chemcl Rectos Itertve or ppromte methods or systems o equtos cosst o guessg vlue d the
THEORY OF EQUATIONS OBJECTIVE PROBLEMS. If the eqution x 6x 0 0 ) - ) 4) -. If the sum of two oots of the eqution k is -48 ) 6 ) 48 4) 4. If the poduct of two oots of 4 ) -4 ) 4) - 4. If one oot of is
New bounds on Poisson approximation to the distribution of a sum of negative binomial random variables
Sogklaaka J. Sc. Tchol. 4 () 4-48 Ma. -. 8 Ogal tcl Nw bouds o Posso aomato to th dstbuto of a sum of gatv bomal adom vaabls * Kat Taabola Datmt of Mathmatcs Faculty of Scc Buaha Uvsty Muag Chobu 3 Thalad
Chapter 3 Higher Order Linear ODEs
ht High Od i ODEs. Hoogous i ODEs A li qutio: is lld ohoogous. is lld hoogous. Tho. Sus d ostt ultils of solutios of o so o itvl I gi solutios of o I. Dfiitio. futios lld lil iddt o so itvl I if th qutio
1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
r R N S Hobbs P J Phelan B E A Edmeaes K D Boyce 2016 Membership ams A P Cowan D D J Robinson B J Hyam J S Foster A NAME MEMBERSHIP NUMBER
ug bb K S bb h B E E ch Smth K t Sth E ugh m Cw b C w h T B ug bb K C t tch S bb h B E ch Smth K t Sth E ugh m Cw b S B C w Shh T ug bb K C tch S bb h ch Smth K t u Sth E m Cw b h S B C w O Shh T ug bb
l2 l l, i.e., phase k k k, [( ). ( ). ]. l1 l l, r, 2
![l2 l l, i.e., phase k k k, [( ). ( ). ]. l1 l l, r, 2](/thumbs/88/116048903.jpg "l2 l l, i.e., phase k k k, [( ). ( ). ]. l1 l l, r, 2")
ISSN: 77-3754 ISO 9:8 tfd Itto Jou of Egg d Iovtv choogy (IJEI Vou 7 Iu 7 Juy 8 o dft wv gtzd duty cyd Ajy Ghot Dtt of Ad Sc Mhj Suj Ittut of choogy Dh-58 Id d ( x ( x Abtct- h ffct of dut chg fuctuto
PhysicsAndMathsTutor.com
PhysicsAdMthsTutor.com PhysicsAdMthsTutor.com Jue 009 4. Give tht y rsih ( ), > 0, () fid d y d, givig your swer s simplified frctio. () Leve lk () Hece, or otherwise, fid 4 d, 4 [ ( )] givig your swer
Answer: First, I ll show how to find the terms analytically then I ll show how to use the TI to find them.
. CHAPTER 0 SEQUENCE, SERIES, d INDUCTION Secto 0. Seqece A lst of mers specfc order. E / Fd the frst terms : of the gve seqece: Aswer: Frst, I ll show how to fd the terms ltcll the I ll show how to se
Chapter 8: Propagating Quantum States of Radiation
Quum Opcs f hcs Oplccs h R Cll Us Chp 8: p Quum Ss f R 8. lcmc Ms Wu I hs chp w wll cs pp quum ss f wus fs f spc. Cs h u shw lw f lcc wu. W ssum h h wu hs l lh qul h -c wll ssum l. Th lcc cs s fuc f l
Advanced Higher Formula List
Advaced Highe Fomula List Note: o fomulae give i eam emembe eveythig! Uit Biomial Theoem Factoial! ( ) ( ) Biomial Coefficiet C!! ( )! Symmety Idetity Khayyam-Pascal Idetity Biomial Theoem ( y) C y 0 0
N e w S t u d e n t. C o u n c i l M e n
ZV. XX L GG L 3 942. 25 J b D b v D G... j z U 6 b Y DY. j b D.. L......&. v b v. z " 6 D". " v b b bv D v.... v z b.. k."... 92... G b 92. b v v b v b D ( 6) z v 27 b b v " z". v b L G. b. v.. v v. D
Department of Mathematics and Statistics Indian Institute of Technology Kanpur MSO202A/MSO202 Assignment 3 Solutions Introduction To Complex Analysis
Dpartmt of Mathmatcs ad Statstcs Ida Isttut of Tchology Kapur MSOA/MSO Assgmt 3 Solutos Itroducto To omplx Aalyss Th problms markd (T) d a xplct dscusso th tutoral class. Othr problms ar for hacd practc..
glo beau bid point full man branch last ior s all for ap Sav tree tree God length per down ev the fect your er Cm7 a a our
SING, MY TONGU, TH SAVIOR S GLORY mj7 Mlod Kbd fr nd S would tm flsh s D nd d tn s drw t crd S, Fth t So Th L lss m ful wn dd t, Fs4 F wd; v, snr, t; ngh, t: lod; t; tgu, now Chrst, h O d t bnd Sv God
Kummer Beta -Weibull Geometric Distribution. A New Generalization of Beta -Weibull Geometric Distribution
ttol Jol of Ss: Bs Al Rsh JSBAR SSN 37-453 Pt & Ol htt://gss.og/.h?joljolofbsaal ---------------------------------------------------------------------------------------------------------------------------
Linear Prediction Analysis of Speech Sounds
Lr Prdcto Alyss of Sch Souds Brl Ch 4 frcs: X Hug t l So Lgug Procssg Chtrs 5 6 J Dllr t l Dscrt-T Procssg of Sch Sgls Chtrs 4-6 3 J W Pco Sgl odlg tchqus sch rcogto rocdgs of th I Stbr 993 5-47 Lr Prdctv
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
668 Chapter 11 Parametric Equatins and Polar Coordinates
668 Chapter Parametric Equatins and Polar Coordinates 5. sin ( sin Á r and sin ( sin Á r Ê not symmetric about the x-axis; sin ( sin r Ê symmetric about the y-axis; therefore not symmetric about the origin
Housing Market Monitor
M O O D Y È S A N A L Y T I C S H o u s i n g M a r k e t M o n i t o r I N C O R P O R A T I N G D A T A A S O F N O V E M B E R İ Ī Ĭ Ĭ E x e c u t i v e S u m m a r y E x e c u t i v e S u m m a r y
Coordinate Transformations
Coll of E Copt Scc Mchcl E Dptt Nots o E lss Rvs pl 6, Istcto: L Ctto Coot Tsfotos Itocto W wt to c ot o lss lttv coot ssts. Most stts hv lt wth pol sphcl coot ssts. I ths ots, w wt to t ths oto of fft
Extension Formulas of Lauricella s Functions by Applications of Dixon s Summation Theorem
Avll t http:pvu.u Appl. Appl. Mth. ISSN: 9-9466 Vol. 0 Issu Dr 05 pp. 007-08 Appltos Appl Mthts: A Itrtol Jourl AAM Etso oruls of Lurll s utos Appltos of Do s Suto Thor Ah Al Atsh Dprtt of Mthts A Uvrst
07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
DRAFT. Formulae and Statistical Tables for A-level Mathematics SPECIMEN MATERIAL. First Issued September 2017
Fist Issued Septembe 07 Fo the ew specifictios fo fist techig fom Septembe 07 SPECIMEN MATERIAL Fomule d Sttisticl Tbles fo A-level Mthemtics AS MATHEMATICS (7356) A-LEVEL MATHEMATICS (7357) AS FURTHER
Asymptotic Dominance Problems. is not constant but for n 0, f ( n) 11. 0, so that for n N f
Asymptotc Domce Prolems Dsply ucto : N R tht s Ο( ) ut s ot costt 0 = 0 The ucto ( ) = > 0 s ot costt ut or 0, ( ) Dee the relto " " o uctos rom N to R y g d oly = Ο( g) Prove tht s relexve d trstve (Recll: