Page 99 - Math Grade 12 (Advance)

PROEUS DARA
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n. dj x(t) ctl13'glti5fn~1:Hl5 P ~w9qb~ru:tbHli t tSHtru~s&sm~~H'159mfd

~61 P ~x'(t) '1
"' I
tt::hrutru~EtSH~Sb a tsmt?'i"QlS x'(t) =a tL:.ib\5 x'(t) ctltL:.i1t~&s x(t)
~ , M dx
M~filJ x (t) =a ffiuMHMaw1 - =a
dt
3 ~ ~ dx
tw~J?lru1Sl13'glti5m x(t) Qh~ru:tnru t t?l1_!i~n:tHLnflti5M~fil~ -d =a
1 U f
dx o~ o ~ o " ~
dt =a Sl'\j dx = adt tthti5JnffibtnLfilrutrnH~mb 2 tSM'efil~

t?'i"QlS : J dx = J adt

x(t) = at+ c

t?'i'i.:flS x(t) = at+ c

r;tir;sir;nru t = o ttfiru P 'i:flSu'glru 2m mtg'iifirn o 'i:flssrum t = o, x = 2

&Slgtfi"QlS x(O) = a(O)+c ttnru x(O) = 2 tSlg c = 2
dx
• eJ
Ql
Ql
':t
Q)
"
Ql
L:.imsg x(t) = at+2 ctlumti5~ti5t8M~fil~~tdab&MJb15 -d =a nbn~rul
u ., 1.1 t '1
""
(t=O,x=2) ttit=3 tSUx(3)=3a+2'1
" M~fila x'(t) =a t'UlirtlM~filJ~td~b~MJb15rutnti9 1 ~L:.ib\5'i:f1S91Jb~r;gj
dy = f(x)
dx
.. Hsr:m@ x(t) = at+c t'Ulimm~ru9t9i&sM~fil~~r;nHHM~ru x'(t) =a
1 6V u t.l
cr ~ ':t e» t::.'l} ~~
"HS?'i~S x(t) = at+2 ctlm~ti5~ti5tSM~filanbn~rul (t=O, x=2) tu11Gl
I N 1.1 «
I
m~rutltMMtSM~fil~~td~b~M~b\5rutnti9 1 ffl~b\5n~rult~~ x(O) = 2
"" t.l 9 9
~mJutr:fUUU1IDN1§m~~tnftH'NJru'i:fiEH~~ci ~~ = f(x)

" MHMa dy = f(x) ctl dy = f(x)dx
dx
"~nffibtnLfilrnH~mbna: Jdy= f!Cx)dx t{y= fJ(x)dx+c, cctl~~sr;tl~

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