Page 253 - Math Grade 12 (Advance)

PROEUS DARA
t::lo Or. 0 •
ffifiJi1§8fii:I!Uii§iU816J

" WiJt'i : j(x) 'i::flS nHhi L ffH1H1.JTI 0 < lx- ai < 8 ==> if(x)- Ll < E

1 + -
: e = lim ( I)" = 2. 71828
11-7+~ n
" f1tit'i! : (all) t:tH~n~'i:HIThn A ttl lim all = A
, u ~ 1J ll-7+=

"1M'i!ffltuitnifStiUUtMtf: m(b-a)$f(b)-j(a)$M(b-a)

" t]ii!Wt : F(x) mu;~g{fs f(x) mrurun F'(x) = f(x)
r" [ Jb
0
'
0
• ffibltil.,fnfl111Mt'i : t j(x)dx = F(x) a = F(b)-F(a)
.... , lr"
" tiCJU1fJ'iltSH1f1!iUS : y m = b _ aJ J<x)dx
a
" mnthti :· J<x> mul!'~ a !~/<x> = J<a>

• Hlf1!iURmnm1ertsfn : f(x) = lnx

"tYti1n : (a 11 ) t:h~n1nt9i~n ±co ttl lim a = ±oo
B 1 n-7+ oo 11
" r.Jfiuejm : ttl f(a) = f(b) &S'H'i::flS c e (a, b) ti::l ru f'(c) = o

" Mbtt'il.,FnflJiJJUfllntf : f f(x)dx = F(x) + c

" Mbttif.FJf11tfMtfltfU!Jfgn : r · jg'dx = [t · g] b -r gj'dx
a a a
.. lgl..nfPmumbttil.,Fnmnnnti : s = l t<x)dx
a 2
" m:zlBfiJWt'ifi1tgtf'I!!J (x'x) : v = 1t r[ J(x) J dx

• Mlmtfttddf11.!Jfl1Wtsflimmti9 1 : y' + ay = o

" Mlr:ntftdidfi1.!Jfl1Wtsflimmti9 1 i1Sff{MS : y' + ay = p(x)
" t:JRlsHtsttt:Jt : m9Slri9 stutlbnt'l§ts9ss rutnmtflusbnt't§ts9s s rutH1H9'n
"' "" ... 1.1 u 6U co 1.1 'J

n I/iYi _ L,xlL/i
: a=
nL,x;-(L,x;r

b = ~ ( LY;-aL,x; )

11 M'lJumlfft~lSHtdt X : E(x) = ~>1 p1 , i = 1, 2, ... , n

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