![Formulario de Prec´ . · PDF file11) R tanudu = ln[secu] = −ln[cosu]+C 12) R cotudu = lnsenu 13) R secudu = ln[secu+tanu] = ln u tan au u 2 + π 4 14) R cscudu = ln[cscu−cotu]](https://static.fdocument.org/doc/165x107/5aba216c7f8b9ac1058ea568/formulario-de-r-tanudu-lnsecu-lncosuc-12-r-cotudu-lnsenu-13-r.jpg)
dx =x = x exdx =e x - puskice.org izvoda: Funkcija f (x) Izvod f (′x) c =const 0 x 1 xα αxα−1...
2
Tablica izvoda: Funkcija ( x f Izvod (x) f ′ const c = 0 x 1 α x 1 - α αx x a a a x ln x e x e x a log a x ln 1 x ln x 1 x sin x cos x cos x sin - tgx x 2 cos 1 ctgx x 2 sin 1 - x arcsin 2 1 1 x - x arccos 2 1 1 x - - arctgx 2 1 1 x + arcctgx 2 1 1 x + - Površine ravnih figura: = b a dx x f P ) ( , ′ ⋅ = 2 1 ) ( t t t dt (t) x t y P , = β α ϕ ϕ ρ d P ) ( 2 1 2 . Tablica integrala: + = c x dx c n x dx x n n + + = + 1 1 + = c x x dx ln + = c e dx e x x c a a dx a x x + = ln + - = c x xdx cos sin + = c x xdx sin cos c tgx x dx + = 2 cos c ctgx x dx + - = 2 sin 1 2 2 1 1 c a x arcctg a c a x arctg a a x dx + - = + = + , 0 ≠ a c a x a x a a x dx + + - = - ln 2 1 2 2 , 0 ≠ a c a x x a x dx + ± + = ± 2 2 2 2 ln , 0 ≠ a 1 2 2 arccos arcsin c a x c a x x a dx + - = + = - , 0 > a c x tg x dx + = 2 ln sin c x tg x dx + + = ) 4 2 ( ln cos π c a x a x a x dx x a + + - = - arcsin 2 2 2 2 2 2 2 , 0 > a c A x x A A x x dx A x + + + + + = + 2 2 2 ln 2 2 Dužina luka krive: dx x f l b a ′ + = 2 )) ( ( 1 , dt t y t x l t t t t ′ + ′ = 2 1 2 2 )) ( ( )) ( ( , ϕ ϕ ρ ϕ ρ β α d l ′ + = 2 2 )) ( ( ) ( . Zapremina obrtnih tela: = b a dx x f V ) ( 2 π , ′ ⋅ = 2 1 ) ( 2 t t t dt (t) x t y V π , = β α ϕ ϕ ϕ ρ π d V sin ) ( 3 2 3 . Površina omota a obrtnih tela: ′ + = b a dx x f x f P 2 )) ( ( 1 ) ( 2 π , dt t y t x t y P t t ′ + ′ = 2 1 2 2 )) ( ( )) ( ( ) ( 2 π , ϕ ϕ ϕ ρ ϕ ρ ϕ ρ π β α d P sin )) ( ( ) ( ) ( 2 2 2 ′ + = .
Transcript of dx =x = x exdx =e x - puskice.org izvoda: Funkcija f (x) Izvod f (′x) c =const 0 x 1 xα αxα−1...
Tablica izvoda:
Funkcija ( )xf Izvod (x)f ′
constc =
0
x
1
αx 1−ααx
xa aa x ln
xe
xe
xalog ax ln
1
x ln x
1
xsin
xcos
xcos
xsin−
tgx x2cos
1
ctgx x2sin
1−
xarcsin 21
1
x−
xarccos 21
1
x−−
arctgx 21
1
x+
arcctgx 21
1
x+−
Površine ravnih figura: �
=b
a
dxxfP )( , � ′⋅=2
1
)(
t
t
t dt(t)xtyP , �=β
α
ϕϕρ dP )(2
1 2 .
Tablica integrala:
�+= cxdx
cn
xdxx
nn +
+=
� +
1
1
�+= c x
x
dxln
�+= cedxe xx
ca
adxa
xx +=
�ln
�+−= cxxdx cossin
+= cxxdx sincos
ctgxx
dx +=
2cos
cctgxx
dx +−=�
2sin
122
11c
a
xarcctg
ac
a
xarctg
aax
dx +−=+=+
�, 0≠a
c ax
ax
aax
dx ++−=
−
ln
2
122 , 0≠a
c axx ax
dx +±+=±
�22
22ln , 0≠a
122
arccosarcsin ca
xc
a
x
xa
dx +−=+=−
�, 0>a
c x
tg x
dx +=�
2ln
sin
c x
tg x
dx ++=�
)42
(lncos
π
ca
xaxa
xdxxa ++−=−
�arcsin
22
22222 , 0>a
c Axx A
Axx
dx Ax +++++=+�
222 ln22
Dužina luka krive: dxxflb
a
�′+= 2))((1 , dttytxl
t
t
tt
�′+′=
2
1
22 ))(())(( , ϕϕρϕρβ
α
dl � ′+= 22 ))(()( .
Zapremina obrtnih tela: �=b
a
dxxfV )(2π , � ′⋅=2
1
)(2t
t
t dt(t) xtyV π , �=β
α
ϕϕϕρπd V sin)(
3
2 3 .
Površina omota� a obrtnih tela: �
′+=b
a
dxxfxfP 2))((1)(2π , dt tytxtyP
t
t
�′+′=
2
1
22 ))(())(()(2π , ϕϕϕρϕρϕρπβ
α
d P sin))(()()(2 22�
′+= .
Maklorenove formule:
)(!)1(
...!2!1
112
xR n
x
x
xe n
nx +
−++++=
−, x
! )( θe
n
xxR
n
n= , Rx ∈<< ,10 θ .
)(! )12(
)1(...! 5! 3! 1
sin12
121
53
xRn
xxxxx
n
nn
+
−− +
−−+−+−= , x
n
xxR
nn
n cos
! )12( )1()(
12
12θ
+−=
+
+ , Rx ∈<< ,10 θ .
)(! )22(
)1(...! 4! 2
1cos2
221
42
xRn
xxxx
n
nn +
−−+++−=
−− , x
n
xxR
nn
n cos
! )2()1()(
2
2θ−= , Rx ∈<< ,10 θ .
)()1(
)1(...4321
)1ln(1432
xRn
xxxxxx
n
nn +
−−++−+−=+
−
, n
nn
n xn
xxR
) 1( )1()( 1
θ+−= + , 1110 ≤<−<< x ,θ , .1>n
)() 1 (...) 2 () 1 () 0 ()1( 12 xRxnxxxn
n +−++++=+ −ααααα , nnn
xxnxR −+= αθα ) 1() ()( , , 10 << θ 1< x ,
!
)1)...(1() (
k
kk
+−−= αααα , R∈α , } 0 {0
∪=∈ NNk ;
:1=α )()1(1
1 1
0
xRxx n
kkn
k
+−=+ �
−
=1n x)1(
)1()(
++−=
θ
nn
n
xxR , , 10 << θ 1 <x .
Trigonometrija:
yxyxyx sincoscossin)sin( +=+
yxyxyx sinsincoscos)cos( −=+
tgytgx
tgytgxyxtg
⋅−+
=+1
)(
ctgyctgx
ctgxctgyyxctg
+−=+ 1
)(
yxyxyx sincoscossin)sin( −=−
yxyxyx sinsincoscos)cos( +=−
tgytgx
tgytgxyxtg
⋅+−=−
1)(
ctgxctgy
ctgxctgyyxctg
−+=− 1
)(
2cos
2sin2sinsin
yxyxyx
−+=+
2cos
2cos2coscos
yxyxyx
−+=+
yx
yxtgytgx
coscos
)sin( +=+
yx
yxctgyctgx
sinsin
)sin( +=+
2cos
2sin2sinsin
yxyxyx
+−=−
2sin
2sin2coscos
yxyxyx
−+−=−
yx
yxtgytgx
coscos
)sin( −=−
yx
xyctgyctgx
sinsin
)sin( −=−
xxx cossin22sin =
xxx 22 sincos2cos −=
xtg
tgxxtg
21
22
−=
ctgx
xctgxctg
2
12
2 −=
[ ])sin()sin(2
1cossin yxyxyx ++−=
[ ])cos()cos(2
1sinsin yxyxyx +−−=
[ ])cos()cos(2
1coscos yxyxyx ++−=
2
cos1
2sin 2 xx −=
2
cos1
2cos 2 xx +=
21
22
sin2 x
tg
xtg
x+
=
21
21
cos2
2
xtg
xtg
x+
−=
xtg
xtgx
2
22
1sin
+=
xtgx
22
1
1cos
+=
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