smart solution mtk

8/7/2019 Smart Solution Mtk

1/30

I t l lAA tt lDrDr(Al@PNIMAEAMA'6rrl"f^ /^/^.* f.u464,;krmiE, 1 Feb 2ooB

r4abeic- uNA5 / tPMB

A. \Ar,+Wn ULanaq Pertavnaan Kuctdrae, ?er+iActksavna'lY\ kuadraEq In1t)nome*Li) bar'rsan dan Dereto) Lin,t olan Differer|ialo) ?er1avnC^A^qTn( lYtr! S, V ksVonen olc'n l'ogavlt r"tc'^'c Nqiar rua^9 VvgtzuP

B. WaLew gelzundera7 PtLaE' clart Funql+i) lYatnkso> feLttc.tng)) Staa;hkcJ Loctrka (hanYc+ Ur!As )

C. Maten tPt l, ln &qtalo1 Drrnasivr9^q Yek-boYa) 1'rAVSfo(ma91

KantorPusat: GRAHAPRIMAGAMAJf. Diponegoro89 YogyakartaTelp.(02741548U3,520418Ext. 116Faks.(0274)548436,521482


2/30

o ?cnso,^rorsn $s7ri5 l^truSvelaLtu 6, i , t l ' ( , (W,,9,) dunqan gruclrcn r4?ers. qYe LuruS qangConvoh'-Itntukr.rn Pe" gls W m[L

YenyeLesaianL ----tm=-) 5 ,---1

t t *s lL,?urngOtx t Ilu ngo, 9 )

rneLatui

hvtL" Lz, l ) c lengun

l Laac,n lctndctJA^-99=-]t /v| 2,4)

,Y: ,= 49qv^c.rdien

cl eng cn.r

al' ! =d \

J

Pers g,rt 'yprv5 ya^g molaLut ahl'


3/30

?ers.gvs.W mclalui Lit; i l / ' (K, ,9,) olan L d& qrt Lz'enOLW,.TenYuian Pers' qJ( Ub mlf ' (q") daw -L donVanr ix+ 72=tz I?enyeLeSatan

r----\4x+ 9Y =\-:'rnelnLui (

VeL:?. ; berLukaran

5 mQr+ tt2 a-

Lavsan tanda Y

/, ,2

4't)

?e.rs.grt. U9 rneLoiut Ahh LI ' ' 9' ) dornCodc:oh,

Cx, vr)

d.an Cz'6) tAenvuVan?enleletatan

lers- qrs- ytu nn[t . Ls,q)5Yrrar t I

9 _.,_ 4/\2 ' 679 - Gz)x " 22

atau zL7v =2>


4/30

all^!rtsPnfttffitilfi'6./"f^. /^1^* f,uaa*;Li . t u

Unwl* LimiE, gg pa\nq Verlu hrxus *nu *urunctn.irnarL :

),Va 9U) = \f6 , \raVotJtf-t

g'cx)= -#n V /'(") n-'Cun+ult :t Frnxl l

Drnt 4t

L.rrr"tl4-

22V4Izz1zlJsx-t -{?x+t7x -L

zx- 69 x +to

q2V4 -t IA

-7- 2V151

3= -- ro

=9 3Va +vt

akar koelesrcn delc^n

KantorPusat: GRAHAPRIMAGAMAJf. Diponegoro89 YogyakartaTelp.(0274)548443,520418Ext.116Faks.(0274)548436,521482


5/30


6/30

:al . r.gPililIETilT'Ar/"""t /^b,^*@

o |f ta *evdaTav qo'Denqan Y'rubal^cLvr"

(*enk-oel^ 1gin (qo +t)@e 1qo + 6)r/^^ (qo + ot)

6Yau 3 6b"Stw --')LotLan ----1cov

-2 waVa Vrtrbalt(ns


7/30

gPNftIIETIIIA=Ad"f^- /t(^r"* @ )uvn'"r t , A treb 'oB

ln tr qraLA, \nu,eqraL lak lenW unu)|1 ?ctngl l-ar ' ?ecnl+

Con+PV suflara!

( . tA rC

ln VeqtraL SubhLust'Lontph ttmavL'.

(nU \ Vsx+a dx/r

' l ^+= + (gx+?) +s3,5

drIJfw

l,+twnVen "'

dx=Lr t !lcx+t8 )


8/30

Ad.'p.1' /ala/- ?rta6a';ta

lnV"grol Suloh+u9-. fursel,ts'uh satL^6wtoh gmarL t

,?cvtgVae rambah Sau

)G/ tr" ,+ro) dx =+ (rn,+ro) '+"Cpnu>{, Ven YQnq tasren :O t?x" (r*r+E) ' , tx/.\ ( Axlzt I - - Av) ( tx '+r?)3

(rr t + rr)+-3(zx' +t+1

sx'+q)-

r .1LIgx '+tt) ctx?r a r7(9X-+u/ *6

-7 24

I 8x)Bl-rL t

tc

dx

(t J zx dx= ( ,^)3tg

@ LAr =; ; (n^*z)- +c

KantorPusat: GRAHAPRIMAGAMAJf. Diponegoro89 YogyakartaTelp.(0274)548443,520418Ext. 116Faks.(0274)548436,521482


9/30

:41.r !

inVeqral Ynqonow*w ' seList"h SotuC,ntoh ttf ictrL I brar nltan

t- .Lt- +a) dx

- ConboW I'


10/30

V. Vua: d'" tort;aln l*urta

. 9(l '- ,,\no$'u/l\l ' Ov-,n$v- . \ \V .N'\o(}'

z,^ f - : 5. r ,8 = g

r - L. z.B = tbe3

KantorPusat: GRAHAPRIMAGAMAJl. Diponegoro89YogyakartaTelp.(0274)548443,520418Ext. 116Faks.(0274)548436,521482


11/30

g?HilTTTTI'6ul?. /^12, - fro6a,;

L=: 7.8 =82+\, r /Lua5 )^nqu^ neqahy' l-lno- -'

lzalo 9v\ ir"i - ?baay" L doeLoe"'

Ll = L't- l ' tI - ! . 6-I = 3vL'2-

- tL '-3

t . 4, t . 6

L = 4i

KantorPusat: GRAHAPRIMAGAMAJl. Diponegoro89 YogyakartaTelp.(0274)548443,520418Ext. 116Faks.(0274)548436,521482

L.= tL>=L-

- rJ-r t


12/30

g?SIIIIIETilAAd"f^- /^b* fe;

LVamTle'.

L uas di a+.as kurva

L = j- .2 ' tBaqtdu" luf ' - ' '| -L, t . I "LLr- 3 ,L, : i .8 ' t t 4-z

.LL"17Kantor Pusat: GRAHAPRIMAGAMAJl. Diponegoro 89 YogyakartaTelp. 10274154843,520418 Ext. 116

(6=- 3

SmarL :

Faks. (0274)548436,52'1482


13/30

gHBffiTEAilA'6r/"f- /a/a^* f424A4.1,

LtLL_

z-3- -L-L

.2.4 ,9+3. z- = 3

f

6. LuaS kurva Yang d* fuWs, fumbux

v =s+

Y'Lx-t


14/30

cru'Ad."".- /tL* Ttaa*;L. * .2. t = t |

@

Y z l


15/30

cltiltlttl'Ar/"f." //a^- fra64fH. Luas diai.*ara &'n kurva

o fmqr.t Jolrr{r6n:, 9'1trL= 6azTrend saaldengan

u^N / t?M8azl Aanp = 1,1,9,16t25,96," '

Supet Smare tkunct Ja'^:aban

!6L3

+ =1ttlo ?'

,"236


D


16/30

cru'Ad.7. //^ " fuaAl,tfu+oh,0 Htyunglnh Ltas dqerah gqn? di htai kurva

Y, *- zx dan v = 6x-x1?engeVsaia":

*-zx = 6x -/LztrL-Bx= o -

lod i , L= '# t

P = f-4oc= 64' 1Q)b)={1

= 9!.3

@ ?1rc,-urglnqL Va "' lni kale'-'beraya, YoD"- l -ua ' ^Ye-"(e ngclesatan :

)x 't '* +x'*9

6 a.86.4

= -X+4:o: r 4e) f4)' -g

Y=+7Ldan J:-X+t l

r - 0'16v 6az = g'3; = 16.+tl



17/30

ePBrnffirruOd."t- //..* fta64+uqg'sbt a

i.(,

L uas dt bauoh .fung1[ twgonomeln

IT=7@

@

Jl . Diponegoro89 YogyakartaTelp.(02741548M3,520418Ext. 116

\-rt 9 '/-5\A

Faks. (0274)548436,521482


18/30

Sr8rnrllnrAd."t" //^^*ffu)Q&.olt0 , 4Lt - l, 'v . t

l= L2 .3.*,rL

h: ,n '9 ' : ' i lnAt '5 'wn L= - l

frlc latd. L dcvtAh rtt = |z .r)= -X+ LL

titrt< ?cg Lt^d Sb. ! -+ x=ow- )lL

| = L.A - L. kurva= i 'n '+ -z = 1-,Kantor Pusat : GRAHA PRIMAGA-MA 4 -Jf . Diponegoro 89 YogyakartaTelp. (02741548U3,520418 Ext. 116Faks. (0274)548436, 521482


19/30

Cffi'ad.f^." /.L-- frfutLAfT 6KvL

It*zqnl ?arsiqlconlbahnga:

() I x cdtx axrL) [ r^t si,. x ax)

t) I r^ ' e* dx)

htegml subtifurrAt^eoh-tr90''

( .t) | X cosx'dx

t) ( ,r, si", 2)t ax( , | r tt ) | +* 'e 'n dx

F'to sc\dto'VoF' 27azO J'n", cost .r,.t.L1L4

Lt

tox .too '-

zr dx

sin t-x @bsz^ O

bs L7 (9

7 t ' t t^z^+ tnsLl - lcaLx+C



20/30

cru'Ad.f^.- //- *fe@ dx3x

l\ .u3..

4t'_L15Lt5

?(a x+a) '+ (qx+a)9.'

dr =+ qtLt

(t+ o)o& ,I ' *

o rlet ' lx+q dxt \t l t ' , ' f, r r . . r ,o*.., ' ! (x*i lT s, ", . + ? (^*a)7+o '\ 'A.r .L 77r++) '3 -5

1d, ,

ooc

Inr',rG dv=WA^'r@ ' tx' 'F'l . + $'$ *.KantorPusat: GRAHAPRIMAGAMAJf. Diponegoro89YogyakartaTelp.(O274154843,520418Ext. 116Faks. (0274) 548436, 521482


21/30

Coy.Eoh:al ;-\,^r t* dx i + et* +c,K" e* d^t ttox ex

totoe^

TI pr @s x dx)- ^*mtsol : '=t ^dt o e'- 6x

t l \ t t @tx axvt sinx

ex cosx A,x ' e^. sti, x fe* os x dx = c* (s in x + -s x)

et bex o *^lro7!u*f,ti*irlJfi,Jloo"oJl. Diponegoro89 YogyakartaTelp.(0274)548443,520418Ext. 116Faks.(0274)il8436, 521482

= ?- ' ( r* ' - lox +ro ) * c

, gx.it^t- f "^

0()o

in x ctxsU

P=o^d?= e^dxAn= sin rdaL = -coS Xcos x dxJ",

salmr

xe c6sxJz\I


22/30


23/30

lm.Ad."..' /tl--. fue.* gnrclft fotu+tov1Ll/.--


24/30

o@-2,A .21- )-a-, lm.,:1'< J.Jq+tca I :)) DereE hn l, rnad ka

A) V, C + A+C = zBv PereL 6eom14tl

A, g, C 4

iq(^rt 5o(u&on 4:-nUn = 6 --t 9-

AC = b'

#

CD^boW'.DtueLohd dcteL

,t .bala 'San ni t4 I

leng"S- =]-c^ --?t - f

a ' | ( r - r )?-?-^

4r

^t a-l

Vonvergen dengav-r lunolah 1 - Ht+unglah

alLqn honvergem, 'it^" lr | < tS'hXt _l

- l-7

o 1aKantor Pusat : GRAHA PRIMAGAMAJl. Diponegoro89 YogyakartaTetp.(02741S4g4/;3,520419Ext. 116Faks. (0274)548436,521482


25/30

aru'6.1?e-15*# ! Par Sotr.rprag:

C.onboh t

O 1iu"@ )'t'


26/30


27/30

.e"n gOt3 taLr 'r l 'v

Misal kan )al 'u" . da; Pehnggian t \ MQQr' 9an9 fehapVo6 nrnantul menloyai t'za''tggian t daYl kthnqQi

a't| . . \ , _ ' t ' , -1n bola TluS)lervruta. Ia


28/30

iDm'Artpe.lsa9;f lscral

A - 'TurunanfYnart :

CptnLoh;O ru)

funtult

16) = ax +bcx +ar t ; t ad- be7t\1 =at - '

(ex+a) '

9x+4>f+)

15 -g(zx+ Y)r

7Axa+w/+ 9

+G) 3 { i 'no4t+z3.2.2 - 3.t ' 4

Cxt+ity''{*1=0

a, /-.l

lz4Yt { _- l"al*k 'a'n



29/30

:,:-. :- : I r=::: -=:zl::: _t:- l-::- ::::::-r" ' : . \ ' '

o\ j ' - ' ,- ' --

u,oila.l?U*7,r;b. Iurunan

fwiart :

9=langkat z Lugonomct* )

wlil


30/30

^---- t -a.lf lJ-.rf-

C. Nain, Tuyun. 5+at 'ronerO Nark -----+ 7' 'G) )o(, Turctn' ----2 f 'U) f \(x) =o

1u'ttSoo

'12ni"sKaitoner " 'o lax, ' in" f tcx)zo

fu.l1i--,-l. id, t ' 'Lx)=a

rr t^, YLa f ' {x1 to

Actt

dat't

dam

/" Lx)

smart solution mtk

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