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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" http://www.exponenta.ru/educat/free/free.asp -;5:B@>==K9 :C@A ?> Maple V:  HYPERLINK "http://ural.openet.ru/Assets/aMATH0011/soder.htm" http://ural.openet.ru/Assets/aMATH0011/soder.htm #G51=8: 11 :;0AA0 ?> <0B5<0B8:5. . 5;LA:5@, . 5?<0==, ". 5?<0==, "0;;8==, 1999 Kokkuvtte Minu t teemaks on  ppematerial 11. klassi pilastele Maple kasutamiseks matemaatikakursuses  . Selle kursuse material on vlja ttatud informaatika tundide jaoks, mis toimuvad parallelselt teemaga  Arvu logaritm matemaatika tunnides. ppekursus on jaotatud 11 akadeemiliseks tunnis. See materjal kujutab endast praktilist juhatust analtiliste arvutuste paketi Maple vimalustesse. ppematerial koosneb kmnest osast. Esimene osa  Maple lhike iseloomustus , on nagu eessna kogu tle. Siin antakse ssteemi lhike iseloomustus, tema keelte, pakketide kirjeldus, ja ka tema vrdlus sarnaste ssteemidega. Otsekohe mratatakse kasutajate ring:- Maple on matemaatiline ssteem kikidele, ja teda on vimalik kasutada lihtsate lesandade lanendamiseks koolis vi likoolis, ning ka keeruliste objektide modeleerimiseks. Edasi ppematerjal on jaotatud kuueks osaks, mille petamine arvestatud 11 akadeemiliseks tunniks. Kik tunnid sisaldavad tunni eesmrgi, teoteetilise osa, praktilised ja kontrollivad lesandad, metoodilised soovitused. Kik praktilised lesanned petaja selgitab ja pilased teevad tema abiga. Kotrolllesanded sooritavad pilased isesesvalt. Nite, kuidas toimub petamine minuga kirjutatud ppemateriali abil, sooritas 11 klassi pilane Dmiti Vorobjov. Kik temaga tehtud td on kirjas. Material tema jaoks ei olnud keeruline rakendamisel, ja oli vga kasulik tema ppeprotsesis. 1 tund. See on kige mahukam tund. Tunnis andakse kasutajaliidese taielik kirjaldus. Praktikas oli kasutatud osa ksklustest. Tielik kskluste kirjaldus on siin esitatud eesmrgiga, et pilasel tekiks tielik kujutus ssteemist Maple ja tema vimalustest tuleviku ssteemi iseseisval rakendamisel. ksikasjalik Maple abissteemi tutvustus annab vimaluse leida kogu vajaliku informatsiooni. Selle tunni praktilised lesanded petavad ssteemi kivitama, vahetama re~iimi, ttama teksti re~iimis ja salvestama failid. Metoodilised soovitused sisaldavad praktilise t kohta vormistamise ja salvestamise reeglid. Selle tunni materjali petamiseks on vaja 2 akadeemilist tundi. 2 tund Tunni teema:  Maple keele sntaksis Tunni eesmrk on Maple keele ja sntaksiga tutvustamine. Teoretilises osas on esitatud ainult sellised operaatorid, standardsed funktsioonid ja andmetbid, millesed on rakedatud lesande  Arvu logaritm teema juures lahendamisel. Selle materjali ppimisene on arvestatud kahele akadeemilisele tunnile. Siin on ka kirjeldatud tpilised vead, mis tekkivad lesannete titmisel. Aga sellised vead tulevad ette ainult esialgse Maple kasutamisel, ja edasi ts pilane ise neb neid ja parandab. 3 tund Tunni teema:  Matematilise avaldise hindamine Tunni eesmrgiks on anda avaldise miste Maples, ja lbi ttada lihtsate lesanne lahendamise ssteemis abil arvu logaritmi miste. Selle tema pitamisele ette mratud 1 akadeemiline tund. Kik lesanded on valitud tema  Arvu logaritmi miste baasil. Kik funktsioonid ja operaatorid, mis kohtuvad lesannete lahendamisel, on esitatud tundide 1, 2 teoreetilises osas. Oluline siin mrata, et pilane saab vrdleda logaritmid ja mrata neid mrke peas, ja Maple abiga kontrillida oma tulemused. 4 tund Tunni teema:  Logaritmvrrandite lahendamine Teoretiline osa sisaldab kskude kirjaldused logaritmvrrandite lahendamise jaoks. Neid kske vib ka rakendada teist tpi vrrandite lahendamisel. Siin ksitletakse ka erisuguseid vastusi vljapanekuid Praktiliste lesannete abil pilane pib lahendama logaritmvrrandit ja vlja arvutama vastuse. Selle teema ppimisele on arvestatud 2 akadeemilist tundi. 5 tund Tunni teema:  Logaritmi vrratuse lahendamine Tunni eesmrk on tutvustada logaritmi vrratuse lahendusmeetodiga, ka ppida interpriteerima vastuseid. Siin on oluliseks see, et pilane saab nidata kui kiiresti toimub logaritmi vrratuse lahendus. Selle ssteemi kasutamine on kasulik tulemuste kontrolliks igalt tpi lesannete juures. Selle teema petamiseks on arvestatud 1 akadeemiline tund. 6 tund Tunni teema:  Logaritmfunktsiooni graafiku skitseerimine (ehitamine) ssteemis Maple Selle viimase tunni eesmrk logaritmfunktsiooni graafiku skitseerimine ksu plot abiga. Teoreetlises osas vaadeldakse selle ksu olulised parameetrid, millised on pandud tabelisse. Praktilises ts pilased pevad ka tegema tekstikommentaare ja vlja viima erinevaid objektid hele joonisele. Veel tunnis ksitletakse, kuidas lahendada graafiliselt logaritmi vrratused. Selle teema materjal on vga kasulik logoritmi teooria petamisel, selleprast, et joonisel on ilusti nha, kuidas vlja neb funktsiooni graafik. Selle materjali petamiseks on arvestatud 2 akadeemilist tundi. Kontrollt Kontroll t koosneb 6 lesandest, mis hlmavad kogu pitud materjali. Selle t titmiseks on mratud 1 akadeemiline tund ja lubatakse kasutada konspekte ja varem lahendatud lesandeid. Dmitri tegi selle t edukalt, ja tal lks ligikaudu 40 minutit selle jaoks. See rgib sellest, et pitud materjali ta vttis omaks. Kuidas ta sooritas kontroll t vib vaadatad praktilises ts. Ssteemi Maple omandamine oli vga kasulik Dima jaoks, ja ta kavatseb tulevikus ka kasutada seda. Kik praktilised td tehakse Maple 10 versioonis. Juba esimesest tunnis pilased mrkavad, et ssteemiga on mugav lahendada erinevaid lesandeid. See vtab vhe aega, ja kiiresti vib saada vastused. 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