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12 x 3 6 x 2
2 x 2
p
x 1
2 4
p
x 3
% 2 x ( x 4 2 x 2 +1)
ln x +1 3 x 2 cos x + x 3 sin x
( x 4 +1) 2
1 ln x
x 2
1
sin 2 x
ln( x 2 +1)+ 2 x 2
x 2 +1
2 e x 1
4 x 3 cos(ln(1+ x 4 ))
1+ x 4
3
4 x 2 ( x 3 1) 5 4
/ %
p
x 1
( x 1) 2
% e x 2 (2ln x +4 x 2 ln x 2 x 2 )
%
p
x +1
(2ln x ) 2
f 0 ( x ) = 3( x 2 +2 x 4) 7 8:9<;>=@?@ACBEDF;FG@HJI ;LK x 1 = 1 p
5 9 x 2 = 1+
p
5 7
x =
p
5 1 ],P^BXU_?‘9OPRQ,PTS<HVUWBXSON,;XK x = 1 p
5 a
f 0 ( x )=4 x ( x 2 +3 x 4) 7#8M9O;>=@?@ACBbDF;cG‘HJI ;LK x 1 =1 ] x 2 =0 ] x 3 = 4 7d8M9ON,9<P^B
x = 4 9 x =1 ]hPiBXU_?@9<PRQ,PS<HXULBLS<N,;LK x =0 a
f 0 ( x )= 3 x 2 +2 x 7)8M9<;f=@?‘AFBjDc;FG‘HJIk;XK x 1 = 2 3 9 x 2 =0 7l8M9<N 9<PRQ,PmS<HVUWBXSON,;nY[Q,N,ULA>=@9\K
x =0 ],P^BXU_?‘9OPRQ,PoSOHVUWBXS<N ; x = 2 3 7
f ( x ) = x 3 3 x 2 +3 x 1 7qp f 0 ( x ) =3( x 2 x +1) 7r8:9<;>=@?@ACB:DF;FG@HJI ;LK x 1 = 1 7
f 0 ( x )= e x 2 x (4 x 2 ) 7d8M9<;f=@?‘AFB Dc;FG@H € Ik;XK x 1 =2 ] x 2 =0 ] x 3 = 2 7d8M9<N 9<PRQ,P
f 0 ( x ) = e x 2 (1 x 2 ) 7 ‚ 8:9<;>=@?@ACB ƒ Dc;FG@H € Ik;XK x 1 = 1 ] x 2 = 0 ] x 3 = 1 7 „ 8M9<N 9<PRQ,P
x =0 ]hPiBXU_?@9<P^B S<HVUWBXSON,; x = 1 9 x =1 a
7
x =0 ]hPiBXU_?@9<P^B S<HVUWBXSON,; x = 2 9 x =2 a
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13
q
a =
5 2 +(12 x ) 2 7
5
a
9 u}B XHVGwBX?‘B ,HV?vu}B € =@;cP zV]
3 a
5 x 7
12−x
x
A
x 2 [0;12] 7
DFBX? ˆ P^BXG@?‘DFQ H ?‘DFHX?‘9<;LK
12
T ( x )= x
5 + 1
q
uw; XH HLuwG‘D zlPRQW=@;FP ztY[Q,N,ULA>= XK
5 2 +(12 x ) 2 x 2 [0;12] :
3
T 0 ( x )= 1
5
12 x
3
q
25+(12 x ) 2
G‘D z)G@xJI NlQ € = XA H)A}| H ,N H Dc;FG‘B HXu‘G‘D z)P QW=@;FP z K
12 x = 3
4
5
T (0)= 1 3 ] T (12)= 5 3 + 1 5 9 T (8 1 4 )= 8 1 5 + 6 1 3 HXu‘G‘D z)P^BXP zX]
x 2 [0;12] I z) ‰ 9<;FG‘BXP z G‘HVD I 9 XDFBXN,9<; x = 12 1 4 7
HVG‘xJI N_QW= XA I BXG@u‘H ‘Ac9
; HX?@u}BWuwN,9<B^InBLG@uwH ˆ =@;F?vu
y 2 =
15 t 30 ‰ H I A}|{I 9<SO9 t =0 DFN,B € = ,HJInB ,?@9 H "! # P 9<S G‘DF; $ ,Q N,U{uw;FP A 7 &% ˆ‰ {z DFNhBXSO; ’$ kP 9<N,9 (
y 1 =10 t 7
H H
;FN,9O; f?‘Dc; VH ?@uwBLuwU_Q~K
H H
;FN,9O; ,G‘Q X9<; XH ?vu}BLu‘U_Q~K
P^BXS<N ) H * ,S<; $ H X],I zl?vu}BXG@AFDcz ƒ DFNhBLS<; ’$ P 9<N 9<PRQ,PTU{InB GwBLu‘Q H S<; * H @AF9g7h8M9<N,9OPiBLS<9<DcQW=@;FP z
DCBWuw;FPTY[Q,N,UXAf=
d ( t )= y 2 1 + y 2 2 =15 2 ( t 2) 2 +10 2 t 2 t 2 [0 ; + 1 )
9<AcD , XA - H)A}|,H * ,N ) ,HV?vu}B € =@;cP z
t = 1 13 7
d 0 ( t )=450( t 2)+200 t 7
G‘DczlG@x € I N_QW= LA = . H Dc;FGwBjHXuwG@Dcz /
d (0)=900 d ( 18
13 )= 46800
277 lim
t ! + 1
d ( t )=+ 1
169
" ˆ‡
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;k?@uwBLuwU_9 ‰ ZNhB € =@ ‰ ,SO9
;f= HZHVU 7
VH DX7W9
! P^9ONlQ)u}BXA}|~]LBeH * ,S<; $ H kI u‘; z
Š
I zlN,9<;c?‘9O;jHXUXH H
6"
q
0
= K (100 2 a )
2
‰ ,SO9<AFDFBXP z &HlA}|,H * ,N )
W 0 ( a )=
Ka (100 a ) 25 K
q
Ka (100 a )
:
p
a =0 7
W (0)= W (100)=
25 K B W (50)=50
K 25 K > W (0) I N,9<HV?@U_QW=@;FP zX]
G‘D z)G@xJI NlQ € = XA &HlA}|,H * ,N ) HRDF;cGwBRHXu‘G‘DczlPRQ € =@;FP z K
; PiBXU_?vz)P^BXSONhBiI z * hB € =@N,H
DFHX?@u}BLN,9<; HV?@9 VN,9 cu}B ztI P 9<;c?‘DFBXN,9<N 9<;e ‰ DF9<; # uwSO;FN_Q~7
„ "
P 0 ( I )=100 44 I:
‰ ,S<9OAFDFBXP z HlA}|,H N ) P H)A z I † DCBLS<;
N,H @AF9 H ^NhBLu
I = 110
44 = 2 ; 5 7
P (0) = 0
G‘D z)G@xJI NlQ € = XA &HlA}|,H * ,N ) ,H Dc;FGwB HXu‘G‘D z)P QW=@;FP z
lim I ! + 1 P ( I )= 1 PiBXP zV]
I = 2 ; 5 P^HlA ,G N,9<A z ‰ $ ,DF9O;^N,B € =vI 9 cUl?@DCB ƒ 9
DCB
; ,S B
6"
y 0=1( x 0)
= ) y = x
y 1=0( x 0)
= ) y =1
y 1
2 = 1
2 ( x ln2) = ) y = x
2 + 1
p
p
p
2 (ln2+1)
p
2
2 =
2
2
x
4
2
2 x +
2
2
1
4
y
= ) y =
y 1=0( x 1)
= ) y =1
y 0=1( x 0)
p
( x p
= ) y = x
p
y 0=2
) = ) y =2
x 2
!
!
y ln2
1
2 e
ln2
e
1
2 e
ln2
e
( x 2)+ ln2
e
e =
( x 2) = ) y =
/ %
„ "
P (2 ; 5)=137 ; 5 7
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"
ln y + z
x ; ln z + x
y ; ln x + y
#
3+ln2 ; 1
2 +ln3 ; 2
$&% r f ( x;y;z )
=
z
=
3
(1 ; 2 ; 3)
(1 ; 2 ; 3)
% r f ( x;y )
=[2(cos( xy )+ x )(1 y sin( xy )) ; 2 x (cos( xy )+ x )sin( xy )]
1
2
(1 ; 2 )
(1 ; 2 )
=
2
; 2
"
x ln( yz )+ 1
y
!
;e xy 1
z
#
ln2 ; 1 ; 1
2
()% r f ( x;y;z )
=
ye xy ln( yz ) ;e xy
=
(0 ; 1 ; 2)
(0 ; 1 ; 2)
h
% r f ( x;y;z )
=
( x + y + z )( z ( x + y + z )+2 xz ) ;
(1 ; 2 ; 1)
i
2 xz ( x + y + z ) ; ( x + y + z )( x ( x + y + z )+2 xz )
=[ 8 ; 4 ; 0]
(1 ; 2 ; 1)
2719780.029.png 2719780.030.png 2719780.031.png 2719780.032.png

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