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1 PhysicsAdMthsTuto.com

2 5. () Show tht d y d PhysicsAdMthsTuto.com Jue 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*

3 PhysicsAdMthsTuto.com Jue 009 Questio 5 cotiued blk *M3544A038* 3 Tu ove

4 PhysicsAdMthsTuto.com Jue 00. The displcemet metes of pticle t time t secods is give by the diffeetil equtio Whe t = 0, = 0 d d dt =. d cos = 0 dt Fid Tylo seies solutio fo i scedig powes of t, up to d icludig the tem i 3 t. (5) blk 4 *N35388A044*

5 PhysicsAdMthsTuto.com Jue 0. blk () Show tht, whee k is costt to be foud. (3) Give tht, t d, (b) fid seies solutio fo y i scedig powes of, up to d icludig the tem i. (4) 4 *P3543A048*

6 PhysicsAdMthsTuto.com Jue 0 5. blk () Show tht () Give tht y = t =, (b) fid seies solutio fo y i scedig powes of i., up to d icludig the tem (8) *P4004A08*

7 PhysicsAdMthsTuto.com Jue 0 Questio 5 cotiued blk *P4004A038* 3 Tu ove

8 PhysicsAdMthsTuto.com Jue 03 (R) 4. Give tht blk d y y d dy 5y 0 d = () fid d 3 y 3 d i tems of d y d, d y d d y. (4) Give tht y = d d y d = t = 0 (b) fid seies solutio fo y i scedig powes of, up to d icludig the tem i 3. (5) *P4955A03*

9 PhysicsAdMthsTuto.com Jue 03 (R) Questio 4 cotiued blk *P4955A033* 3 Tu ove

10 PhysicsAdMthsTuto.com Jue 03 blk 3. Give tht y d y 4y si = 0 d y = d d = t = 0, d 8 fid seies epsio fo y i tems of, up to d icludig the tem i 3. (5) 6 *P4349A068*

11 Futhe Pue Mthemtics FP Cdidtes sittig FP my lso equie those fomule listed ude Futhe Pue Mthemtics FP d Coe Mthemtics C C4. Ae of secto A = dθ (pol coodites) Comple umbes θ e i = cosθ isiθ { (cosθ isiθ )} = (cos θ isi θ ) k i e π The oots of z = e give by z =, fo k = 0,,,, Mclui s d Tylo s Seies ( ) f( ) = f(0) f (0) f (0) f (0)!! ( ) ( ) ( ) f( ) = f( ) ( ) f ( ) f ( ) f ( )!! ( ) f( ) = f( ) f ( ) f ( ) f ( )!! e = ep( ) =!! 3 l ( ) = ( ) 3 fo ll 3 5 si = ( ) 3! 5! ( )! 4 cos = ( )! 4! ()! 3 5 ct = ( ) 3 5 ( < ) fo ll fo ll ( ) Edecel AS/A level Mthemtics Fomule List: Futhe Pue Mthemtics FP Issue Septembe 009 9

12 Futhe Pue Mthemtics FP Cdidtes sittig FP my lso equie those fomule listed ude Coe Mthemtics C d C. Summtios = = 3 = = 6 4 ( )( ) ( ) Numeicl solutio of equtios The Newto-Rphso itetio fo solvig f( ) = 0 : f( ) = f ( ) Coics Pbol Rectgul Hypebol Stdd Fom y = 4 y = c Pmetic Fom (t, t) ct, c t Foci (, 0) Not equied Diectices = Not equied Mti tsfomtios Aticlockwise ottio though θ bout O: cosθ siθ siθ cosθ Reflectio i the lie cos θ si θ y = (tθ ) : si θ cos θ I FP, θ will be multiple of Edecel AS/A level Mthemtics Fomule List: Futhe Pue Mthemtics FP Issue Septembe 009

13 Coe Mthemtics C4 Cdidtes sittig C4 my lso equie those fomule listed ude Coe Mthemtics C, C d C3. Itegtio ( costt) f() f( ) d sec k t cot t k k l sec l si cosec l cosec cot, l t( ) sec l sec t, l t( 4 π ) dv du u d = uv v d d d Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C4 Issue Septembe 009 7

14 Coe Mthemtics C3 Cdidtes sittig C3 my lso equie those fomule listed ude Coe Mthemtics C d C. Logithms d epoetils e l = Tigoometic idetities si ( A ± B) = si Acos B ± cos Asi B cos( A ± B) = cos Acos B si Asi B t A ± t B t ( A ± B) = ( A ± B ( k ) t A t B A B A B si A si B = si cos A B A B si A si B = cos si A B A B cos A cos B = cos cos A B A B cos A cos B = si si π ) Diffeetitio f() t k sec cot cosec f( ) g( ) f () k sec k sec t cosec cosec cot f ( )g( ) f( )g ( ) (g( )) 6 Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C3 Issue Septembe 009

15 Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C Issue Septembe Coe Mthemtics C Cdidtes sittig C my lso equie those fomule listed ude Coe Mthemtics C. Cosie ule = b c bc cos A Biomil seies ) ( b b b b b = ( ) whee )!!(! C = = < =, ( ) ( ) ( ) ( ) ( ) Logithms d epoetils b b log log log = Geometic seies u = S = ) ( S = fo < Numeicl itegtio The tpezium ule: b y d h{(y 0 y ) (y y... y )}, whee b h =

16 Coe Mthemtics C Mesutio Sufce e of sphee = 4π Ae of cuved sufce of coe = π slt height Aithmetic seies u = ( )d S = ( l) = [ ( )d] 4 Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C Issue Septembe 009