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K?>;=5=85 :064>3> 7040=8O A;54C5B =0G8=0BL A B5:AB>2>3> :><<5=B0@8O: 040=85 N. 5@54 2K?>;=5=85< :>=B@>;L=KE 7040=89 A;54C5B =018@0BL 2 B5:AB>2>< @568<5 >=B@>;L=K5 7040=8O. >A;5 >:>=G0=8O 2K?>;=5=8O @01>BK =5>1E>48<> A>E@0=8BL D09; A> 2A5<8 2K?>;=5==K<8 7040=8O<8 =0 48A:. <O 20H53> D09;0 =018@05BAO 2 2845: $0<8;8O_N, 345 C:07K205BAO 20H0 D0<8;8O 8 N  =><5@ B5<K. &5;L C@>:0 1: 03@C60BL A8AB5<C Maple 8 2K?>;=OBL ?@>ABK5 7040=8O A =59 2 @568<5 480;>30. =0:><AB2> A> A?@02>G=>9 A8AB5<>9 Maple =0:><AB2> A 2>7<>6=>ABO<8 2840 8=B5@D59A0 8 4>:C<5=B0. #:070=85: 0: ?@>8AE>48B 2 ?@>3@0<<5 Maple @01>B0 A ?@8<5@0<8 40==>3> C@>:0 <>6=> ?>A<>B@5BL 2 ?@0:B8G5A:8E @01>B0E (?@0:B8G5A:0O @01>B0 !1). #@>: 2 "5<0 C@>:0: !8=B0:A8A O7K:0 Maple /7K: Maple (8;8 Maple-O7K:) O2;O5BAO >4=>2@5<5==> 2E>4=K< O7K:>< >1I5=8O A Maple 8 O7K:>< 55 ?@>3@0<<8@>20=8O. E>4OI85 2 =53> A@54AB20 (?@5645 2A53> >?5@0B>@K 8 DC=:F88) ?>4>1@0=K =0AB>;L:> ?>;=> 8 C40G=>, GB> ?@8 @5H5=88 ?>402;ONI53> 1>;LH8=AB20 B8?>2KE <0B5<0B8G5A:8E 7040G >B ?>;L7>20B5;O =5 B@51C5BAO 7=0=89 4065 >A=>2 ?@>3@0<<8@>20=8O. ;O @5H5=8O =C6=>9 7040G8 >1KG=> 4>AB0B>G=> A>AB028BL 0;3>@8B< 8 ?>4>1@0BL =01>@ =C6=KE 4;O 53> @50;870F88 DC=:F89 8 8=KE A@54AB2 Maple-O7K:0.  B> 65 2@5<O Maple-O7K:  >48= 87 A0<KE <>I=KE O7K:>2 ?@>3@0<<8@>20=8O <0B5<0B8G5A:8E 7040G, A>45@60I89 ?>GB8 3000 >?5@0B>@>2, :><0=4 8 DC=:F89, 2E>4OI8E 2 O4@>, >A=>2=CN 181;8>B5:C 8 ?0:5BK DC=:F89 Maple. @8 MB>< >B=>AOI0OAO : B@048F8>==><C ?@>3@0<<8@>20=8N G0ABL Maple-O7K:0 @50;87>20=0 A ?><>ILN 4>2>;L=> A:@><=>3> =01>@0 A?5F80;L=KE 7=0:>2 8 70@575@28@>20==KE A;>2. >;LH8=AB2> DC=:F89 Maple (2 G0AB=>AB8, 2A5, 2E>4OI85 2 ?0:5BK) =0?8A0=K =0 MB>< O7K:5. >MB><C 7=0=85 MB>3> O7K:0 O2;O5BAO >?@545;ONI8< 2 A5@L57=>< 87CG5=88 Maple (A<. [1], C@>: 5). ;D028B Maple-O7K:0 A>45@68B 26 <0;KE ;0B8=A:8E 1C:2 (>B 0 4> z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x:=4);= >?5@0B>@ @025=AB20 4;O 7040=8O @025=AB2 8 ;>38G5A:8E CA;>289 (=0?@8<5@, a=b), C:070=8O >1;0AB59 87<5=5=8O ?5@5<5==KE (=0?@8<5@, i=1..5) 8 7=0G5=89 ?0@0<5B@>2  >?F89 2 DC=:F8OE 8 :><0=40E (=0?@8<5@, color = black);;; ?CAB>9 >?5@0B>@; :: C:070B5;L B8?0 ?5@5<5==>9 (=0?@8<5@. n::integer);-> A>740=85 DC=:F88 (?@8<5@. f:=(x)->tan(x));\ 7=0: >1@0B=>3> 45;5=8O, :>B>@K9 8<55B <=>65AB25==K5 7=0G5=8O 2 7028A8<>AB8 >B :>=B5:AB0.2 >=AB0=BK 8 2=CB@5==85 DC=:F88 >=AB0=BK 2 Maple 1K20NB F5;>G8A;5==K<8, G8A;0 A ?;020NI59 70?OB>9 8 >1K:=>25==K<8 4@>1O<8. @><5 MB8E B8?>2 :>=AB0=B ACI5AB2CNB :>=AB0=BK A 70@575@28@>20==K<8 8<5=0<8  false, true, Pi 8 B0 40;55. !B0=40@B=K5 DC=:F88. @82545< ?@8<5@ <0B5<0B8G5A:>9 70?8A8 2 Maple =5:>B>@K9 AB0=40@B=KE DC=:F89. A5 >=8 4C1;8@CNBAO :=>?:0<8 =0 ?0;8B@5 Palettes (View). abs(a) <>4C;L G8A;0;exp(a) ex;ln(a),log[10](a),log[b](a); ln a, log10 a (lg x 8;8 log a), logb a;sqrt(a), (a)^(1/n), (a)^(b).  EMBED Equation.3 , EMBED Equation.3 , EMBED Equation.3 ;Pi, exp(1)  EMBED Equation.3 .3 "8?K 40==KE &5;K5 (integer)  Maple 2K@065=85 ?@8=04;568B : F5;><C B8?C, 5A;8 >=> A>AB>8B 87 ?>A;54>20B5;L=>AB8 F8D@, =5 @0745;5==KE <564C A>1>9 =8:0:8<8 7=0:0<8. '8A;> B8?0 integer <>65B 1KBL :0: ?>;>68B5;L=K<, B0: 8 >B@8F0B5;L=K<. ! F5;K<8 G8A;0<8 2>7<>6=K A;54CNI85 >?5@0F88: =0E>645=85 <>4C;O G8A;0, =0E>645=85 D0:B>@80;0 G8A;0. ;O ?@>25@:8 ?@8=04;56=>AB8 : >?@545;5==><C B8?C A;C68B >?5@0F8O type. @>1=K5 (fraction) @>1=K5 ?@54AB02;5=K 2 2845: EMBED Equation.3  345  EMBED Equation.3  G8A;8B5;L,  EMBED Equation.3  7=0<5=0B5;L 4@>18. '8A;0 A ?;020NI59 AB@>:>9 (float) "8? float 2 A@545 Maple >?@545;5= :0:: ?>A;54>20B5;L=>ABL G8A5;, @0745;5==KE B>G:>9: <integer>.<integer> <integer>. .<integer> C;52K5 2K@065=8O (boolean) ;O @01>BK A 1C;52K<8 2K@065=8O<8 2 A8AB5<5 70@575@28@>20=K A;>20 true 8 false, 8 ?@54CA<>B@5=0 :><0=40 evalf (5E@3, n)  2KG8A;5=85 A;>6=>3> ;>38G5A:>3> 2K@065=8O 2 G8A;5==>< 2845, 345 5E@3- 2K@065=85, 0 n  B>G=>ABL F8D@ 2K2>40 . ><0=40 evalhf (5E@3)  2KG8A;O5B 5E@3 8 2>72@0I05B 2KG8A;5==>5 7=0G5=85 2 G8A;5==>< 2845 A B>G=>ABLN, ?@8ACI59 >1>@C4>20=8N 40==>3> :><?LNB5@0. $C=:F8O type(x, numeric) ?>72>;O5B 2KOA=8BL, O2;O5BAO ;8 E G8A;><. A;8 O2;O5BAO, B> >=0 2>72@0I05B ;>38G5A:>5 7=0G5=85 true (8AB8=0), 0 5A;8 =5B, B> false (;>6L). @0:B8G5A:85 7040=8O : C@>:C 2 0?CAB8B5 Maple. B:@>9B5 D09;, :>B>@K9 1K; A>E@0=5= =0 ?@54K4CI5< C@>:5. 5@52548B5 AB@>:C 2 B5:AB>2K9 @568< 8 =015@8B5 2 =59: @0:B8G5A:0O @01>B0 !2 8 =0720=85 B5<K C@>:0. >A;5 =5 701C4LB5 ?5@59B8 2 @568< :><0=4=>9 AB@>:8. B:@K205< CG51=8: =0 AB@0=8F5 113, @5H05< =><5@0 330 (1, 6, 16); 332 (1, 5, 6, 9). ><5@ 330. KG8A;8B5 7=0G5=85: 1)  EMBED Equation.3 ; 6) e-1,3; 16)  EMBED Equation.3  A B>G=>ABLN 7=0:>2 = 5. ><5@ 332. KG8A;8B5: 1) e5 ( e2; 5)  EMBED Equation.3 ; 6)  EMBED Equation.3 . B:@K205< CG51=8: =0 AB@0=8F5 119, @5H05< =><5@0 350 (1, 10, 8, 13); 353 (1, 17); 354 (7, 8) ><5@ 350. 0948B5 1) log 2 8; 10)  EMBED Equation.3 ; 8) ln e4; 13) EMBED Equation.3 . ><5@ 353. KG8A;8B5: 1) EMBED Equation.3 ; 5) eln 2 + ln 9. >=B@>;L=K5 7040=8O: ><5@ 354 (7, 8), 8 ?@8<5@ A B>G=>ABLN 7=0:>2 = 3. ><5@ 378 (4, 5). >A;5 MB>3> 2 A;54CNI59 AB@>:5 =015@8B5 B5:AB: $09; A 7040=8O<8 ?@0:B8G5A:>9 @01>BK ! 2 A>E@0=5= ?>4 8<5=5<: $0<8;8O_2 #:070=85: 0: ?@>8AE>48B 2 ?@>3@0<<5 Maple @01>B0 A ?@8<5@0<8 40==>3> C@>:0 <>6=> ?>A<>B@5BL 2 ?@0:B8G5A:8E @01>B0E (?@0:B8G5A:0O @01>B0 !2) 5B>48G5A:85 @5:><5=40F88 : C@>:C 2 @5?>4020=85 <0B5@80;0 MB>3> C@>:0 @0AAG8B0=> =0 2 0:045<8G5A:8E G0A0. K1>@ ?@0:B8G5A:8E ?@8<5@>2 ?@>872>48;AO =0 >A=>20=88 B5<K <0B5<0B8G5A:>3> C@>:0 >30@8D< G8A;0 A5 DC=:F88 8 >?5@0B>@K, :>B>@K5 2AB@5G0NBAO ?@8 @5H5=88 ?@0:B8G5A:8E ?@8<5@>2, >?8A0=K 2 C@>:5 2. >;57=> >B<5B8BL ?@>AB>BC 2KG8A;5=8O @07;8G=KE ;>30@8D<8G5A:8E 2K@065=89 8 ?@>AB>BC 2KG8A;5=85 G8A;0 5 2 @07;8G=>9 AB5?5=8. 5:>B>@K5 ?@82545==K5 2 MB>< C@>:5 ?@8<5@K ;53:> 2KG8A;8BL A ?><>ILN :0;L:C;OB>@0 (8=65=5@=>3>) 8 745AL >=8 ?@82>4OBAO A F5;LN >7=0:><;5=8O A8=B0:A8A0 8 >A=>2=KE DC=:F89 ?@>3@0<<K Maple. &5;L C@>:0 2: >7=0:><8BL A Maple  O7K:>< 8 53> A8=B0:A8A><. 0CG8BLAO 8A?>;L7>20BL Maple  O7K: 8 53> A8=B0:A8A =0 ?@>AB59H8E ?@8<5@0E. B@01>B0BL ?>=OB85 ;>30@8D<0 G8A;0 A ?><>ILN @5H5=8O A Maple ?@>AB59H8E ?@8<5@>2. B@01>B0BL ?>=OB8O 45AOB8G=>3> 8 =0BC@0;L=>3> ;>30@8D<0. >2B>@8BL 459AB28O A> AB5?5=O<8 8 G8A;> e. >:070BL ?@58<CI5AB2> 2KG8A;5=8O ;>30@8D<0 G8A;0 ?@8 ?><>I8 ?@>3@0<<K Maple. =0;87 C@>:0 2: 081>;55 G0AB> 2AB@5G0NI85AO >H81:8 C@>:0 1. 1) #?CI5=85 D8:A0B>@0 2K@065=8O ; , 40NI53> 2K2>4 @57C;LB0B0 2 OG59:C 2K2>40. 2) #G5=8: <>65B 701KBL ?5@525AB8 AB@>:C 2 :><0=4=K9 @568< ?@8 =01>@5 :><0=4K. 3) >B5@O A:>1>: ?@8 =01>@5 :><0=4. 4) @8 =01>@5 G8A5; A ?;020NI59 AB@>:>9 2>7<>6=0 >H81:0 ?@8 @0745;5=88 ?>A;54>20B5;L=>AB8 G8A5; (2<5AB> . 22>4OB ,). 5) #?CI5=85 C:070B5;O ?@>3@0<<=>3> :><<5=B0@8O (#). #@>: 3 "5<0 C@>:0: F5=820=85 <0B5<0B8G5A:8E 2K@065=89 K@065=85 (D>@<C;0) 2 A8AB5<5 Maple  MB> >1J5:B, 2?>;=5 A>>B25BAB2CNI89 ACB8 >1KG=>3> <0B5<0B8G5A:>3> 2K@065=8O. => <>65B A>45@60BL >?5@0B>@K, >?5@0=4K 8 DC=:F88 A ?0@0<5B@0<8 K@065=8O 2 Maple <>3CB >F5=820BLAO 8 87<5=OBLAO 2 A>>B25BAB288 A 7040==K<8 <0B5<0B8G5A:8<8 70:>=0<8 8 ?@028;0<8 ?@5>1@07>20=89. 0B5<0B8G5A:0O D>@<C;0 (2K@065=85), =04 :>B>@>9 1C4CB ?@>872>48BLAO ?@5>1@07>20=8O, 70?8AK205BAO 2 A;54CNI59 D>@<5: eq := exp1=exp2; 345 eq  ?@>872>;L=>5 8<O 2K@065=8O (<>65B B0:65 >1>7=0G0BLAO egs), exp1 (<>65B B0:65 >1>7=0G0BLAO expr) CA;>2=>5 >1>7=0G5=85 ;52>9 G0AB8 D>@<C;K, exp2  CA;>2=>5 >1>7=0G5=85 ?@02>9 G0AB8 D>@<C;K. 0AA<>B@8< =5:>B>@K5 >?5@0F88 ?@5>1@07>20=8O <0B5<0B8G5A:8E D>@<C;. K @0AA<0B@8205< =0 MB>< C@>:5 B>;L:> B5 >?5@0F88, :>B>@K5 2AB@5G0NBAO ?@8 2K?>;=5=88 @07;8G=KE 7040=89 =0 B5<C >30@8D< G8A;0. $C=:F8O type (E, positive) 2>72@0I0NB ;>38G5A:>5 7=0G5=85 true, 5A;8 E O2;O5BAO ?>;>68B5;L=K< G8A;>< 8 false, 5A;8 E O2;O5BAO >B@8F0B5;L=K<. $C=:F8O (x, negative) 2>72@0I0NB ;>38G5A:>5 7=0G5=85 true, 5A;8 E O2;O5BAO >B@8F0B5;L=K< G8A;>< 8 false, 5A;8 E O2;O5BAO > ?>;>68B5;L=K<. >=AB@C:F88 A ;>38G5A:8<8 >?5@0B>@0<8: =,(, ( 2>72@0I0NB ;>38G5A:>5 7=0G5=85  :>=AB0=BC true, 5A;8 CA;>285 2K?>;=O5BAO, 8 false, 5A;8 >=> =5 2K?>;=O5BAO. @><5 B>3>, : ;>38G5A:8< >?5@0B>@0< >B=>A8BAO C=0@=K9 >?5@0B>@ not  >= ?@54AB02;O5B ;>38G5A:>5 =5B. ;O 2>72@0B0 ;>38G5A:8E 7=0G5=89 2K@065=89 A MB8<8 >?5@0B>@0<8 8A?>;L7C5BAO DC=:F8O evalb (CA;>285). @0:B8G5A:85 7040=8O : C@>:C 3 0?CAB8B5 Maple. 5@52548B5 AB@>:C 2 B5:AB>2K9 @568< 8 =015@8B5 2 =59: @0:B8G5A:0O @01>B0 !3 8 =0720=85 B5<K C@>:0. >A;5 =5 701C4LB5 ?5@59B8 2 @568< :><0=4=>9 AB@>:8. B:@K205< CG51=8: =0 AB@0=8F5 128, @5H05< =><5@ 381(4). ><5@ 381: #1548B5AL, GB> 2K?>;=O5BAO @025=AB2> 4) log2 10 = log2 3 ( log2 4 ( log2 10. 0?8A0BL >B25B 2 B5:AB>2>< @568<5. B:@K205< CG51=8: =0 AB@0=8F5 132, @5H05< =><5@0 389 (1, 2, 15). ><5@ 389: ?@545;8B 7=0: G8A;0: 1) log4 6; 2) log2 7; 8) loga 0,3. K?8A0BL >B25BK. B:@K205< CG51=8: =0 AB@0=8F5 132, @5H05< =><5@0 390 (1, 2, 8). ><5@ 390. KOA=8BL, GB> 1>;LH5: 1) log2 3 8;8 log2 10; 2) log5 0,9 8;8 log5 4; 8) ln 5 8;8 ln6. K?8A0BL >B25BK. >=B@>;L=K5 7040=8O: ><5@ 389 (5, 7). K?8A0BL >B25B. ><5@ 390 (4, 5). ><5@ 390 (6, 7) !>E@0=8BL @01>BC. #:070=85: 0: ?@>8AE>48B 2 ?@>3@0<<5 Maple @01>B0 A ?@8<5@0<8 40==>3> C@>:0 <>6=> ?>A<>B@5BL 2 ?@0:B8G5A:8E @01>B0E (?@0:B8G5A:0O @01>B0 !3) 5B>48G5A:85 @5:><5=40F88 : C@>:C 3 @5?>4020=85 <0B5@80;0 MB>3> C@>:0 @0AAG8B0=> =0 1 0:045<8G5A:89 G0A. K1>@ ?@0:B8G5A:8E ?@8<5@>2 ?@>872>48;AO =0 >A=>20=88 B5<K <0B5<0B8G5A:>3> C@>:0 >30@8D< G8A;0. A5 DC=:F88 8 >?5@0B>@K, :>B>@K5 2AB@5G0NBAO ?@8 @5H5=88 ?@0:B8G5A:8E ?@8<5@>2, >?8A0=K 2 C@>:5 2 8 3. &5;L C@>:0: 0CG8BLAO 8A?>;L7>20BL Maple  O7K: 8 53> A8=B0:A8A =0 ?@>AB59H8E ?@8<5@0E. >7=0:><8BL A ?>=OB85< 2K@065=8O. B@01>B0BL ?>=OB85 ;>30@8D<0 G8A;0 A ?><>ILN @5H5=8O A Maple ?@>AB59H8E ?@8<5@>2. 0:@5?;5=85 B5<K >30@8D< G8A;0 ?CB5< @5H5=8O ?@0:B8G5A:89 ?@8<5@>2. 06=K< O2;O5BAO B>, GB> CG5=8: <>65B A@02=820BL 8 >?@545;OBL 7=0:8 ;>30@8D<>2 2 C<5 8 A ?><>ILN Maple ?@>25@OBL 8AB8==>ABL A2>8E AC645=89. -B> A?>A>1AB2C5B 3;C1>:><C ?>=8<0=8N ;>30@8D<0 G8A;0. #@>: 4 "5<0 C@>:0: 5H5=85 ;>30@8D<8G5A:8E C@02=5=89 2 Maple ;O @5H5=8O C@02=5=89 2 Maple ACI5AB2C5B C=825@A0;L=0O :><0=40 solve (eqn,var), 345 eqn  C@02=5=85, var  ?5@5<5==0O, >B=>A8B5;L=> :>B>@>9 C@02=5=85 =04> @07@5H8BL.  @57C;LB0B5 2K?>;=5=8O MB>9 :><0=4K 2 AB@>:5 2K2>40 ?>O28BAO 2K@065=85, :>B>@>5 O2;O5BAO @5H5=85< 40==>3> C@02=5=8O. A;8 ?@8 70?8A8 eqn =5 8A?>;L7CNBAO 7=0: @025=AB20 8;8 7=0:8 >B=>H5=8O, AG8B05BAO, GB> solve 8I5B :>@=8 C@02=5=8O eqn = 0. $C=:F8O solve AB0@05BAO 40BL @5H5=85 2 0=0;8B8G5A:>< 2845. ;O ?>;CG5=8O :>@=59 2 G8A;5==>< 2845 =04> 8A?>;L7>20BL DC=:F8N evalf (:>B>@0O 1K;0 >?8A0=0 =0 2B>@>< C@>:5 8 >B@01>B0=0 =0 2B>@>< ?@0:B8G5A:>< 70=OB88) 8;8 convert.(ans, type). '0AB> 1K205B C4>1=> ?@54AB02;OBL C@02=5=85 8 53> @5H5=8O 2 2845 >B45;L=KE >1J5:B>2, >B>645AB2;5==KE A >?@545;5==>9 ?5@5<5==>9. -B> ?>72>;O5B 2 40;L=59H5< 8A?>;L7>20BL ?>;CG5==K5 @5H5=8O 2 4@C38E 2KG8A;5=8OE. ;O MB>3> C@02=5=8N (:><0=45 solve) =04> ?@8A2>8BL :0:>5-=81C4L 8<O name. 0?@8<5@ C@02=5=8O C4>1=> >1>7=0G0BL G5@57 eqn1, eqn2, & ; >@=8 C@02=5=8O C C4>1=> >1>7=0G0BL G5@57 s1, s2, ....  G0AB=>AB8, MB> ?>72>;O5B ;53:> ?@>25@8BL @5H5=85 ?>4AB0=>2:>9 subs (var = solve, eqn), solve  :>@=8 C@02=5=8O, eqn  8AE>4=>5 C@02=5=85 A;8 @57C;LB0B @5H5=8O ?@54AB02;5= G5@57 DC=:F8N RootOf, B> ?>;CG8BL 2A5 :>@=8 <>6=> G5@57 DC=:F8N allvalues. 0AA<>B@8< ?@8<5=5=85 MB8E DC=:F89 =0 :>=:@5B=KE ?@8<5@0E. @0:B8G5A:85 7040=8O : C@>:C 4 0?CAB8B5 Maple. 5@52548B5 AB@>:C 2 B5:AB>2K9 @568< 8 =015@8B5 2 =59: @0:B8G5A:0O @01>B0 !4. >A;5 =5 701C4LB5 ?5@59B8 2 @568< :><0=4=>9 AB@>:8. B:@K205< CG51=8: =0 AB@0=8F5 123, @5H05< =><5@ 361 (1, 2, 6). ><5@ 361: 5H8BL C@02=5=85: 1) log x = 2 log 7 + log 2; 2) log 2  log x = log 3; 6)lnx ln (x  1) = ln 2. #:070=85: ;O @5H5=8O MB8E C@02=5=89 8A?>;L7>20BL :><0=4K solve 8 evalf (?C=:BK 1 8 3 MB>3> C@>:0). B:@K205< CG51=8: =0 AB@0=8F5 123, @5H05< =><5@ 360 (1). ><5@ 360 (1): K@078BL x, 5A;8: log x = 0,51 log a. 5H8BL ?>:070B5;L=>5 C@02=5=85 8 A45;0BL ?@>25@:C. ><5@ 363 (1). (!<>B@8 ?C=:BK 1, 2, 3, 4, 5 MB>3> C@>:0). 5H8BL ;>30@8D<8G5A:85 C@02=5=8O. ><5@ 393 (1, 8), AB@0=8F0 134. 1) log2 x = 4; 8) logx+1 x2 =0. 5H8BL ;>30@8D<8G5A:>5 C@02=5=85 8 A45;0BL ?@>25@:C. ><5@ 395 (2). log2 (x  4) + log3 (x + 2) = log3 7. >=B@>;L=K5 7040=8O: ><5@ 394 (3, 6).  >4=>< 87 C@02=5=89 A45;0BL ?@>25@:C. 3) log (x + 3) = log 2; 6) log x =  log 0,8. ><5@ 396 1) log42 x + log4 x  6 = 0; 2) logx2 16 + 2 logx16  8 = 0. !>E@0=8B5 @01>BC. >A;5 MB>3> 2 A;54CNI59 AB@>:5 =015@8B5 B5:AB: $09; A 7040=8O<8 ?@0:B8G5A:>9 @01>BK ! 4 A>E@0=5= ?>4 8<5=5<: $0<8;8O_4 #:070=85: 0: ?@>8AE>48B 2 ?@>3@0<<5 Maple @01>B0 A ?@8<5@0<8 40==>3> C@>:0 <>6=> ?>A<>B@5BL 2 ?@0:B8G5A:8E @01>B0E (?@0:B8G5A:0O @01>B0 !4) 5B>48G5A:85 @5:><5=40F88 : C@>:C 4 @5?>4020=85 <0B5@80;0 MB>3> C@>:0 @0AAG8B0=> =0 2 0:045<8G5A:8E G0A0. K1>@ ?@0:B8G5A:8E ?@8<5@>2 ?@>872>48;AO =0 >A=>20=88 B5<K <0B5<0B8G5A:>3> C@>:0 >30@8D<8G5A:85 C@02=5=8O. A5 DC=:F88 8 >?5@0B>@K, :>B>@K5 2AB@5G0NBAO ?@8 @5H5=88 ?@0:B8G5A:8E ?@8<5@>2, >?8A0=K 2 C@>:5 2 8 4. &5;L C@>:0: 0CG8BLAO 8A?>;L7>20BL >A=>2=CN :><0=4C solve ?@8 @5H5=88 ;>30@8D<8G5A:8E C@02=5=89 8 C@02=5=89 A>45@60I8E 7=0: ;>30@8D<0. 7CG8BL @07;8G=K5 2>7<>6=>AB8 2K2>40 @5H5=8O. B@01>B0BL =>2K9 <0B5@80; ?@8 @5H5=88 2 Maple @07;8G=K9 C@02=5=89. 06=K< O2;O5BAO B>, GB> CG5=8: <>65B C1548BLAO ?@>AB>B5 @5H5=8O 2 ?@>3@0<<5 <=>38E ;>30@8D<8G5A:89 C@02=5=89. A?>;L7>20=85 ?@>3@0<<K O2;O5BAO ?>;57=K< 4;O ?@>25@:8 @57C;LB0B>2 ?@8 A0<>AB>OB5;L=>< @5H5=88. "0:65 >B<5GC B>, GB> ?@8 CA?5H=>< CA2>5=88 <0B5@80;0, CG5=8: A<>65B @5H0BL @07;8G=K5 284K C@02=5=89. A;8 ?@8 @5H5=88 C@02=5=8O 2>7=8:05B =5 @0AA<>B@5==K9 =0 C@>:5 2>?@>A, B> 4;O >B25B0, CG5=8: <>65B 2>A?>;L7>20BLAO A?@02>G=>9 A8AB5<>9 Maple (A?>;L7>20=85 A?@02>G=>9 A8AB5<K @0AA<0B@820;>AL =0 C@>:5 1). #@>: 5 "5<0 C@>:0: 5H5=85 ;>30@8D<8G5A:8E =5@025=AB2 2 Maple @8 @5H5=88 =5@025=AB2 ?@8<5=O5BAO B0:65 :><0=40 solve. @8 MB>< =5@025=AB20 7040NBAO B0: 65, :0: 8 @025=AB20, B>;L:> 8A?>;L7CNBAO 7=0:8 A@02=5=8O. 5H5=85 =5@025=AB20 2K405BAO 2 2845 8=B5@20;0 87<5=5=8O 8A:><>9 ?5@5<5==>9.  B>< A;CG05, 5A;8 @5H5=85 =5@025=AB20 ?>;C>AL, B> 2 ?>;5 2K2>40 ?>O2;O5BAO :>=AB@C:F8O 2840: ReaiRange ( ", Open (a)), :>B>@0O >7=0G05B, GB> x ( ( ", a), 345 0  =5:>B>@>5 G8A;>. !;>2> Open >7=0G05B, GB> 8=B5@20; A >B:@KB>9 3@0=8F59. A;8 MB>3> A;>20 =5B, B> A>>B25BAB2CNI0O 3@0=8F0 8=B5@20;0 2:;NG5=0 2> <=>65AB2> @5H5=89. 5H5=85 =5@025=AB20 B0:65 <>6=> ?>;CG8BL 2 2845 >3@0=8G5=89 4;O 8A:><>9 ?5@5<5==>9 2 2845: a ( x, x( b, B> ?5@5<5==CN, >B=>A8B5;L=> :>B>@>9 =C6=> @5H8BL =5@025=AB2>, A;54C5B C:07K20BL 2 D83C@=KE A:>1:0E {}. 0AA<>B@8< @5H5=8O ;>30@8D<8G5A:8E =5@025=AB2 =0 :>=:@5B=KE ?@8<5@0E. @0:B8G5A:85 7040=8O : C@>:C 5 0?CAB8B5 Maple. 5@52548B5 AB@>:C 2 B5:AB>2K9 @568< 8 =015@8B5 2 =59: @0:B8G5A:0O @01>B0 ! 5. >A;5 =5 701C4LB5 ?5@59B8 2 @568< :><0=4=>9 AB@>:8. B:@K205< CG51=8: =0 AB@0=8F5 132, @5H05< =><5@ 391 (1, 4, 10). K?8A0BL >B25BK 2 B5:AB>2>< @568<5. 1) log2 x ( 0; 4) log0,7 x ( 0; 7) ln (x2  1) ( 0; 9) log0,6 [(8 x + 7)/(7 x - 6)]; 10) log 2x ( 1. >=B@>;L=K5 7040=8O: ><5@ 391 (5, 6, 13, 14). 5) log (x  5) ( 0; 6) log (1  x) ( 0; 13) log0,1 x (  1; 14) log0,3 (x + 5) ( 2; !>E@0=8B5 @01>BC. >A;5 MB>3> 2 A;54CNI59 AB@>:5 =015@8B5 B5:AB: $09; A 7040=8O<8 ?@0:B8G5A:>9 @01>BK ! 5 A>E@0=5= ?>4 8<5=5<: $0<8;8O_5 5B>48G5A:85 @5:><5=40F88 : C@>:C 5 @5?>4020=85 <0B5@80;0 MB>3> C@>:0 @0AAG8B0=> =0 2 0:045<8G5A:8E G0A0. K1>@ ?@0:B8G5A:8E ?@8<5@>2 ?@>872>48;AO =0 >A=>20=88 B5<K <0B5<0B8G5A:>3> C@>:0 >30@8D<8G5A:85 =5@025=AB20. A5 DC=:F88 8 >?5@0B>@K, :>B>@K5 2AB@5G0NBAO ?@8 @5H5=88 ?@0:B8G5A:8E ?@8<5@>2, >?8A0=K 2 C@>:5 2 8 4. &5;L C@>:0: 0CG8BLAO 8A?>;L7>20BL >A=>2=CN :><0=4C solve ?@8 @5H5=88 ;>30@8D<8G5A:8E =5@025=AB2. 7CG8BL @07;8G=K5 2>7<>6=>AB8 2K2>40 @5H5=8O 8 =0CG8BLAO 8E 8=B5@?@5B8@>20BL (A MB>9 F5;L 2 7040=8OE C:070=> 2K?8A0BL >B25B). B@01>B0BL =>2K9 <0B5@80; ?> ;>30@8D<8G5A:8< =5@025=AB20< ?@8 8E @5H5=88 2 Maple . 06=K< O2;O5BAO B>, GB> CG5=8: <>65B C1548BLAO ?@>AB>B5 @5H5=8O 2 ?@>3@0<<5 <=>38E ;>30@8D<8G5A:89 =5@025=AB2. 06=K< 745AL O2;O5BAO ?@028;L=>5 B>;:>20=85 2K2>40 >B25B>2. A?>;L7>20=85 ?@>3@0<<K O2;O5BAO ?>;57=K< 4;O ?@>25@:8 @57C;LB0B>2 ?@8 A0<>AB>OB5;L=>< @5H5=88 =5@025=AB2. "0:65 >B<5GC B>, GB> ?@8 CA?5H=>< CA2>5=88 <0B5@80;0, CG5=8: A<>65B @5H0BL =5 B>;L:> ;>30@8D<8G5A:85 =5@025=AB20, => 8 =5@025=AB20 4@C3>3> B8?0. A;8 ?@8 @5H5=88 =5@025=AB20 2>7=8:05B =5 @0AA<>B@5==K9 =0 C@>:5 2>?@>A, B> 4;O >B25B0, CG5=8: <>65B 2>A?>;L7>20BLAO A?@02>G=>9 A8AB5<>9 Maple (A?>;L7>20=85 A?@02>G=>9 A8AB5<K @0AA<0B@820;>AL =0 C@>:5 1). #@>: 6 "5<0 C@>:0: >AB@>5=85 3@0D8:>2 ;>30@8D<8G5A:8E DC=:F88 2 A8AB5<5 Maple Maple  =570<5=8<K9 ?><>I=8: ?@8 ?>AB@>5=88 ;N1KE B8?>2 3@0D8:>2. 0 MB>< C@>:5 <K =0CG8<AO A@>8BL 3@0D8:8 ;>30@8D<8G5A:>9 DC=:F88. ;O ?>AB@>5=8O 3@0D8:>2 DC=:F88 f (x) >4=>9 ?5@5<5==>9 (2 8=B5@20;5 a ( x ( b ?> >A8 OX 8 2 8=B5@20;5 c ( x ( d ?> >A8 OY. A5 G8A;0, AB>OI85 2 8=B5@20;5 4>;6=K 1KBL 459AB28B5;L=K<8) 8A?>;L7C5BAO :><0=40 plot (f(x), x = a..b, y = c..d, parameters), 345 parameters  ?0@0<5B@K C?@02;5=8O 87>1@065=85<. A;8 8E =5 C:07K20BL, B> 1C4CB 8A?>;L7>20=K CAB0=>2:8 ?> C<>;G0=8N. 0AB@>9:0 87>1@065=8O B0:65 <>65B >ACI5AB2;OBLAO A ?0=5;8 8=AB@C<5=B>2. A=>2=K5 ?0@0<5B@K :><0=4K plot ?@82545=K 2 B01;8F5:  " +'/!title =  text  AB@>:0, 345 text-703>;>2>: @8AC=:0 703>;>2>: @8AC=:0 (B5:AB <>6=> >AB02;OBL 157 :02KG5:, 5A;8 >= A>45@68B B>;L:> ;0B8=A:85 1C:2K 157 ?@>15;>2).coordscoords = polar CAB0=>2:0 ?>;O@=KE :>>@48=0B (?> C<>;G0=8N CAB0=>2;5=K 45:0@B>2K5).axes1) axes = NORMAL 2) axes = FRAME 3) axes=BOXED 4) axes=NONE CAB0=>2:0 B8?0 :>>@48=0B=KE >A59: 1)  >1KG=K5 >A8; 2)  3@0D8: 2 @0<:5 A> H:0;>9; 3)  >A8 A F5=B@>< 2 ;52>< =86=5< C3;C @8AC=:0; 4)  157 >A59.scaling1) scaling = CONSTRAINED 2) scaling = UNCONSTRAINED CAB0=>2:0 <0AHB010 @8AC=:0: 1)  >48=0:>2K9 <0AHB01 ?> >AO<; 2)  3@0D8: <0AHB018@C5BAO ?> @07<5@0< >:=0style= LINE (POINT) ?>AB@>5=85 ;8=8O<8 (8;8 ?> B>G:0<8)numpoints = nF5;>5 G8A;> G8A;> 2KG8A;O5<KE B>G5: 3@0D8:0 (?> C<>;G0=8N n = 49)linestyleF5;>5 G8A;> B8? ;8=88: =5?@5@K2=0O, ?C=:B8@=0O 8 B.4. (n = 1  =5?@5@K2=0O, CAB0=>2;5=> ?> C<>;G0=8N)Aolor70@575@28@>20==>5 A;>2> 8;8 ?@>F54C@0 CAB0=>2:0 F25B0 ;8=88: 0=3;89A:>5 =0720=85 F25B0, =0?@8<5@, yellow  65;BK9 8 B.4.xtickmarks = nx ytickmarks = nyF5;>5 G8A;> G8A;> <5B>: ?> >A8 x 8 >A8 y, A>>B25BAB25==>thickness = nn = 1,2,3&  B>;I8=0 ;8=88 (?> C<>;G0=8N n = 1)symbol = sBOX, CROSS, CIRCLE, POINT, DIAMOND B8? A8<2>;0, :>B>@K< ?><5G0NB B>G:8font = [f, style, size][f, style, size] CAB0=>2:0 B8?0 H@8DB0 4;O 2K2>40 B5:AB0: f 70405B =0720=85 H@8DB>2: TIMES, COURIER, HELVETICA, SYMBOL; style 70405B AB8;L H@8DB0: BOLD, ITALIC, UNDERLINE; size  @07<5@ H@8DB0 2 pt.labels = [tx, ty][tx, ty] =04?8A8 ?> >AO< :>>@48=0B: tx  ?> >A8 x 8 ty  ?> >A8 ydisconttrue, false 4;O ?>AB@>5=8O 2K@065=89 A @07@K20<8axesfont[f, style, size] H@8DB 4;O >A59sample[x1, x2, x3,..,xn] A?8A>: B>G5:, 2 :>B>@KE 1C45B ?>AB@>5=0 DC=:F8O! ?><>ILN :><0=4K plot <>6=> AB@>8BL ?><8<> 3@0D8:>2 DC=:F89 y=f(x), 7040==>9 O2=>, B0:65 3@0D8:8 DC=:F89, 7040==KE ?0@0<5B@8G5A:8 y=y(t), x=x(t), 5A;8 70?8A0BL :><0=4C plot([y=y(t), x=x(t), t=a..b], parameters). K2>4 =5A:>;L:8E 3@0D8G5A:8E >1J5:B>2 =0 >48= @8AC=>: '0AB> 1K205B =5>1E>48<> A>2<5AB8BL =0 >4=>< @8AC=:5 =5A:>;L:> 3@0D8G5A:8E >1J5:B>2, ?>;CG5==KE ?@8 ?><>I8 @07;8G=KE :><0=4, =0?@8<5@, 4>1028BL : 3@0D8:C, =0@8A>20==><C :><0=4>9 plot, B5:AB>2K5 =04?8A8, ?>;CG5==K5 :><0=4>9 textplot. ;O MB>3> @57C;LB0B 459AB28O :><0=4K ?@8A208205BAO =5:>B>@>9 ?5@5<5==>9: > p := plot(& ): t := textplot(& ): @8 MB>< =0 M:@0= 2K2>4 =5 ?@>872>48BAO. ;O 2K2>40 3@0D8G5A:8E 87>1@065=89 =5>1E>48<> 2K?>;=8BL :><0=4C 87 ?0:5B0 plots (> ?0:5B0E <>6=> ?@>G8B0BL 2 @0B:0O E0@0:B5@8AB8:0 A8AB5< :;0AA0 Maple  ?C=:B 2): > with (plots): display([p,t], options). !>2<5I5=85 3@0D8:>2 >6=> ?>AB@>8BL =5A:>;L:> 3@0D8:>2 =0 >4=>9 :>>@48=0B=>9 ?;>A:>AB8. ;O MB>3> 4>AB0B>G=> C:070BL 2 :><0=45 plot <=>65AB2> 8;8 A?8A>: DC=:F89, B> 5ABL 70?8A0BL G5@57 70?OBCN DC=:F88 8 70:;NG8BL 8E 2 D83C@=K5 8;8 :204@0B=K5 A:>1:8.  MB>< A;CG05 Maple 02B><0B8G5A:8 2K18@05B @07=K5 F25B0 4;O 3@0D8:>2. @8 =5>1E>48<>AB8 4;O :064>9 DC=:F88 <>6=> C:070BL :>=:@5B=K9 F25B 8 AB8;L ?>AB@>5=8O (A<>B@8 B01;8FC, :>B>@0O ?@54AB02;5=0 2KH5). &5;L MB>3> C@>:0  =0CG8BL AB@>8BL 3@0D8:8 ;>30@8D<8G5A:>9 DC=:F88, 8 2 B5>@5B8G5A:>9 G0AB8 >?8A0=K B5 DC=:F88 8 :><0=4K, :>B>@K5 <>3CB 1KBL ?>;57=K ?@8 ?>AB@>5=88. @8<5G0=85: >?>;=8B5;L=CN 8=D>@<0F8N > 3@0D8:5 2 Maple <>6=> ?>;CG8BL 2 ;N1>< 87 8AB>G=8:>2, C:070==KE 2 A?8A:5 8A?>;L7>20==>9 ;8B5@0BC@K. ! ?><>ILN :><0=4K plot <>6=> @5H0BL 8 ;>30@8D<8G5A:85 =5@025=AB20, 54 2<5AB> DC=:F88 70?8AK205BAO A0<> =5@025=AB2>. 0: >=8 @5H0NBAO @0AA<>B@8< =0 :>=:@5B=KE ?@8<5@0E. @0:B8G5A:85 7040=8O : C@>:C 6 0?CAB8B5 Maple. 5@52548B5 AB@>:C 2 B5:AB>2K9 @568< 8 =015@8B5 2 =59: @0:B8G5A:0O @01>B0 ! 6. >A;5 =5 701C4LB5 ?5@59B8 2 @568< :><0=4=>9 AB@>:8. 040=8O 4;O ?>2B>@5=8O: B:@K205< CG51=8: =0 AB@0=8F5 131, @5H05< =><5@ 383 (1, 7, 10) K?8A0BL >B25BK 2 B5:AB>2>< @568<5. 0948B5 >1;0ABL >?@545;5=8O DC=:F88: 1) y = 6x; 7) y = 2  x; 10) y = log8 x ( 0. ><5@ 384. >AB@>8BL 2 >4=>9 8 B>9 65 A8AB5<5 :>>@48=0B 3@0D8:8 DC=:F89 y = log6x, y = log2 x, y = log1,3 x, y = log1,1 x. 0: 2;8O5B >A=>20=85 ;>30@8D<0 =0 @0A?>;>65=85 3@0D8:0 A>>B25BAB2CNI59 ;>30@8D<8G5A:>9 DC=:F88? @0D8:8 87>1@078BL @07=K<8 F25B0<8. ><5@ 384. . >AB@>8BL 2 >4=>9 8 B>9 65 A8AB5<5 :>>@48=0B 3@0D8:8 DC=:F89 y = logx, y = 2 log x, y = 1+log x. @0D8:8 4>;6=K 8<5BL ?0@0<5B@K: plot([log[10](x),2*log[10](x),1+log[10](x)],x=-1..5,color=[blue,red,yellow],labels = [OX, OY],thickness = 2,symbol = BOX,numpoints = 200,scaling = UNCONSTRAINED,linestyle=[1,5,10],title =  logarifmifunktsioonide_graafikud ); 5H8BL =5@025=AB20 3@0D8G5A:8 8 A ?><>ILN :><0=4K solve.><5@ 391 (2, 8) 2) log3 x( 0; 3) ln (2 x  3) / (4  x) ( 0. K?8A0BL >B25BK. >=B@>;L=K5 7040=8O: ><5@ 383 (2, 5).@0D8:8 87>1@078BL 65;BK< F25B><. 09B8 >1;0ABL >?@545;5=8O DC=:F89: 2) y = 0,3x; 5) y = 0,6 2x. ><5@ 387: >AB@>8BL 2 >4=>9 8 B>9 65 A8AB5<5 :>>@48=0B 3@0D8:8 DC=:F89 y = logx, y = 2 log x, y = 3 log x. 0@0<5B@K: color=[blue,red], symbol = POINT, thickness = 3, title =  logarifmifunktsioonide_graafikud , labels = [OX, OY]. 5H8BL =5@025=AB20 3@0D8G5A:8 8 A ?><>ILN :><0=4K solve.K?8A0BL >B25BK 2 B5:AB>2>< @568<5. ><5@ 391 (3, 11). 3) log 0,5 x ( 0; 11) log (x2 + 36) ( 2. !>E@0=8B5 @01>BC, ?>A;5 70?8A8 2 B5:AB>2>< @568<5: $09; A 7040=8O<8 ?@0:B8G5A:>9 @01>BK ! 6 A>E@0=5= ?>4 8<5=5<: $0<8;8O_6 #:070=85: 0: ?@>8AE>48B 2 ?@>3@0<<5 Maple ?>AB@>5=85 3@0D8:>2 <>6=> ?>A<>B@5BL 2 ?@0:B8G5A:8E @01>B0E (?@0:B8G5A:0O @01>B0 !6) 5B>48G5A:85 @5:><5=40F88 : C@>:C 5 @5?>4020=85 <0B5@80;0 MB>3> C@>:0 @0AAG8B0=> =0 2 0:045<8G5A:8E G0A0. K1>@ ?@0:B8G5A:8E ?@8<5@>2 ?@>872>48;AO =0 >A=>20=88 B5<K <0B5<0B8G5A:>3> C@>:0 >30@8D<8G5A:85 DC=:F8O. A5 DC=:F88 8 ?0@0<5B@K, :>B>@K5 2AB@5G0NBAO ?@8 ?>AB@>5=88 DC=:F89, >?8A0=K 2 B5>@5B8G5A:>9 G0AB8 C@>:0. #<5=85 AB@>8BL 3@0D8:8 M:>=><8B 2@5<O ?@8 87CG5=88 :0: ;>30@8D<8G5A:8E, B0: 8 4@C38E DC=:F89. 0 ?@0:B8:5 AB@>8;8AL 3@0D8:8 2 >A=>2=>< B>;L:> ;>30@8D<8G5A:8E DC=:F89, => A ?><>ILN :><0=4K plot 2>7<>6=> ?>AB@>5=85 ;N1KE 3@0D8:>2. &5;L C@>:0: 0CG8BLAO AB@>8BL 3@0D8:8 ;>30@8D<8G5A:8E DC=:F89 8 Maple A ?><>ILN :><0=4K plot. 0CG8BLAO 45;0BL 2K2>4 B5:AB>2K9 :><<5=B0@852 =0 @8AC=>: 8 2K2>4 =5A:>;L:8E 3@0D8G5A:8E >1J5:B>2 =0 >48= @8AC=>:. 0CG8BLAO 87<5=OBL ?0@0<5B@K 3@0D8:>2. #<5=85 AB@>8BL 8 >1@010BK20BL 3@0D8:8 ;>30@8D<8G5A:>9 DC=:F88 2 A8AB5<5 ?><>305B 1>;55 CA?5H=> CA2>8BL MBC B5<C 1;03>40@O =03;O4=><C ?@54AB02;5=8N. @0D8:8 <>3CB >:070BLAO ?>;57=K<8 ?@8 @5H5=88 C@02=5=89 8 =5@025=AB2, B0: :0: =0 @8AC=:5 284=>, :0: ?@>E>48B 3@0D8: DC=:F88. >=B@>;L=0O @01>B0 "@51>20=8O:  B5:AB>2>< @568<5 225AB8 >=B@>;L=0O @01>B0.  B5:AB>2>< @568<5 225AB8 02B>@0 @01>BK. 5@54 @5H5=85< 22>48BL =><5@ 7040=8O. ! ?><>ILN B5:AB>2>3> :><<5=B0@8O C:07K20BL =><5@ @5H05<>3> ?@8<5@0 5B>48G5A:85 C:070=8O: 01>B0 @0AAG8B0=0 =0 1 0:045<8G5A:89 G0A. @8 2K?>;=5=88 @01>BK @07@5H05BAO ?>;L7>20BLAO :>=A?5:B0<8 C@>:>2 8 @0=55 @5H5==K<8 7040=8O<8. 040=8O: KG8A;8BL: 0) ln 444.9; 1) log100. ?@545;8BL 7=0: G8A;0: 0) log0,83 4; 1) log5 0,49; 2) ln 0,7. K?8A0BL >B25B. 09B8 G8A;> E, 5A;8: 0) ln x = 3,0525; 1) log x =  5,4. 0BL >B25B A B>G=>ABLN 4> 3 7=0:>2. @0D8:8 87>1@078BL 65;BK< F25B><. 5H8BL C@02=5=8O 8 2 >4=>< 87 =8E A45;0BL ?@>25@:C: 0) log3 x + log9 x+ log27 x = 22/3; 1) log2 (x2  3E) = 2. 5H8BL =5@025=AB2>, >4=> =0 2K1>@ 3@0D8G5A:8: 0) log1/2 (2x  3) ( log1/2 (x2  6); 1) log0,5(5x  3) / (E + 2) ( 1.K?8A0BL >B25BK. >AB@>9B5 2 >4=>9 8 B>9 65 A8AB5<5 :>>@48=0B 3@0D8:8 DC=:F89 y = logx 8 y = log3x. !45;0BL =04?8A8 ?> >AO< :>>@48=0B: tx  ?> >A8 x 8 ty  ?> >A8 y, 8 B>;I8=0 ;8=88 n=2 8 225AB8 703>;>2>: @8AC=:0. @0D8:8 87>1@078BL 75;5=K< 8 65;BK<8 F25B0<8 A>>B25BAB25==>. !>E@0=8BL @01>BC ?>4 8<5=5< Vorobjov_7. !?8A>: 8A?>;L7>20==>9 ;8B5@0BC@K ><?LNB5@=0O <0B5<0B8:0 Maple 7 M;5:B@>==K9 CG51=8::  HYPERLINK "http://matclub.ru/Maple7/" http://matclub.ru/Maple7/ 0B5<0B8G5A:89 ?0:5B Maple V Realase 4 C:>2>4AB2> ?>;L7>20B5;O ( 2 D>@<0B5 PDF):  HYPERLINK "http://www.exponenta.ru/educat/free/free.asp" 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