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m8&on16B016DFD$Q20b0B5616p^3C.DFDF*203H->1?,/.783C16B0b,/BG72HFH20O>-*216>-*:,@H20,@*qr:k^sW7'H'DFB00H'5?54*+&
(8H:>1?,@*a54*'3C72BGDF1614313C*-,/.00*214356.78.+16M160O7-Q:_=/Q+U-9CH'7-*dH'0ODd.+H2,/H^*
ax 5 + bx 2 + ce x + d sin x + f
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3CBe3/*'*dH'5654*aBG3C16DFB=/716783C1wM8_>16071603C..=C14*'3,/BG160+BG0OZH'56_0H'DF1lU3C*'*'y*2*20OMBG5?ZH^3z,@1
{
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7.56143,@*'*23C1w>-*'3,@*'*>-*a160^,@B=/ZH'56H'1?>-*aZH'56_0H2DF1l&
} &on1616=C=@QKZ143,/BG143,/pJ7'HH'=@y+1?0*'*-,/143,/HH'0w&(8*-,/.00*2143C56.+78.Z+143,@BB,Y7.>-*'*>-*:,YZ143,/BG14y+B0
y
sW7'HH'=/y+160*'*-,C,/B9C*x
sW7'HH'=/y+160*'*:,/,/16B0OH'5656BG3/3/*a7'H'72H'0*-143C56.7.-9/*8&~8&on1616=C=@QDFH256BGDFD$*:,aZ143z,@B143,/p8p203CH:>1?,/,@*2D$*23C1x7-Q_8=/Q-,a3/*2D$*2*207.>-*'*20w&KMy+143zs
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+&Z+,/16DFH'160^,/1H'0|_7+3C1BG0+1?,@B0|,/16B`,@H27'H'0B1?,<*M_'p8y+_0,@Q>143,@QdD$*:,@BD$*-,/16167-*-0O*256H2143s
,@*+&XY,@3C1u .07^,@16H20
f (x) = x 4 + x 3 − x 2 − x
Da16016DF1w>-Q256165654QbRszmUm:VW&.07^,@16H25654*H207-*-7+31Da16016DF167'H2M,@*'*8&XY,@3C1w0Q2143,@QaDFH'5?BGDFD$*:,&
&on1616=C=@Qu.+07,/16H'0
f (x, y) = x 2 + y 4 7.>-*2*:9/*|7.0
x ∈ [ − 1, 1]
9C*y ∈ [ − 1, 1]
&X ,<31w,@Q2565?BJu.07^,/16H'5656BJDF16016DF1l&
c+&oXY,@3C1u.07^,/16H'5656B
√
x + sin x
9CH'7160O56H272*2*2561wDF16016Da1+9C*9CH278160O56H27-*'*2561wD$*-7+3C16Da1l&+&on1616=C=/B,@Q'Q-0SBG56561?Z3C160
x 2
9 + y 16 2 = 1 3C143/Q2565?B$3C.H2=@*27.56DF1?H& L 1?,/7-QbH:>-*-,3C16>.0SZ1?s ,/..y+B`,U-9H^33C.H2=@*27.56DF16H20OZ160^,<*:sz*-54*aH'0OD$*2My+H'5656143C16DaD$*203C..=C1]
%T+&oXMy+H-,
x − 4y < 6
U2x + 3z > 4
9C*x + y + z < 9
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Q2Q2=/14*-=/>'H-,56160BG*'*2=C143CBG5654*dH'Z8,@16DFH21600165654*8&XY,@3C1,<Q23/3/Qa*256.BB3/3C*aDF160+16DF1u .07^,@1?H'5656B
f(x, y, z) = x + 4y + 6z
&%'%'&567'HH'03C.+H'=@*-78.5?D$*2143CB03/Q2=/Da16p'03C16>.-9CB0[_8M^,/BGB054*'37'B,C,/.[Z160,@*-s*-54*%d0BG5?16p2s
DFB`,/=/1l& L 1?,/BG0S3/Q2=CD$Q-,eH20S>-*-561?,/,@*>-*+UB,C,@QO3/Q-=/DF16p'3,@QO3C*'*'y*2*20,/1654*>..y+B5?,@*'*20
D$*-My+H'565614316DFD$*203C..+=/1]
%:m8&oXY,@3C1KD$*-7+316DF1u .07^,@16H25656B
sin(x + y 2 )
&n1616=C=@QvDd_2p^3u .07^,/16H'0t7.>-*'*9/*7.0x ∈ [0, 2π]
9/*y ∈ [0, 2π]
&wJ*'3C>-*:,<*7.>-*20,<*-=/778.+.+,/,@*g^'k+r8k-sH2Z+,@1?H'5654*9C*aZH2143,@*aZ1600*25,<*a=C..y+.77'H|++:8sWH'Z+,/16H'5656*+&eQ'Q-0,/B56Be7.>-*'*F\'A16BGoZH2160^,
(8B56BN<,/H'=/160d*:>.5654*8&2 ).H'D$*2*-,/7'HKDa167+3C18Q'Q2=C14*2=/>2H-9CB0d54*'37'BGDF1?0BG0d>2H'187-Q_8yQM*-0+s
