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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 10 43 75 73 74 6f 6d | 20 46 75 6e 63 74 69 6f |..Custom| Functio|
|00000010| 6e 73 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |ns......|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00000050| 00 00 00 00 00 05 9a 00 | 00 02 b2 8e f4 9c e8 8e |........|........|
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|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 8e 17 00 00 |........|........|
|00000080| 43 75 73 74 6f 6d 20 46 | 75 6e 63 74 69 6f 6e 73 |Custom F|unctions|
|00000090| 0d 0d 43 75 73 74 6f 6d | 20 46 75 6e 63 74 69 6f |..Custom| Functio|
|000000a0| 6e 73 20 61 72 65 20 6f | 6e 65 20 6c 69 6e 65 20 |ns are o|ne line |
|000000b0| 73 74 61 74 65 6d 65 6e | 74 73 20 69 6e 20 74 68 |statemen|ts in th|
|000000c0| 65 20 66 6f 72 6d 3a 0d | 0d 46 75 6e 28 78 3b 79 |e form:.|.Fun(x;y|
|000000d0| 29 20 3d 20 45 78 70 72 | 65 73 73 69 6f 6e 20 69 |) = Expr|ession i|
|000000e0| 6e 63 6c 75 64 69 6e 67 | 20 58 20 61 6e 64 20 59 |ncluding| X and Y|
|000000f0| 2e 0d 0d 57 68 65 72 65 | 20 3a 0d 22 46 75 6e 22 |...Where| :."Fun"|
|00000100| 20 69 73 20 74 68 65 20 | 6e 61 6d 65 20 6f 66 20 | is the |name of |
|00000110| 74 68 65 20 43 75 73 74 | 6f 6d 20 46 75 6e 63 74 |the Cust|om Funct|
|00000120| 69 6f 6e 2c 20 22 58 22 | 20 61 6e 64 20 22 59 22 |ion, "X"| and "Y"|
|00000130| 20 61 72 65 20 74 68 65 | 20 46 75 6e 63 74 69 6f | are the| Functio|
|00000140| 6e 20 61 72 67 75 6d 65 | 6e 74 73 2e 20 20 54 68 |n argume|nts.  Th|
|00000150| 65 20 46 75 6e 63 74 69 | 6f 6e 20 22 45 78 70 72 |e Functi|on "Expr|
|00000160| 65 73 73 69 6f 6e 22 20 | 69 6e 63 6c 75 64 69 6e |ession" |includin|
|00000170| 67 20 74 68 65 73 65 20 | 76 61 72 69 61 62 6c 65 |g these |variable|
|00000180| 73 20 63 61 6e 20 62 65 | 20 61 6e 79 20 65 78 70 |s can be| any exp|
|00000190| 72 65 73 73 69 6f 6e 2e | 20 20 49 74 20 6d 61 79 |ression.|  It may|
|000001a0| 20 69 6e 63 6c 75 64 65 | 20 6f 74 68 65 72 20 46 | include| other F|
|000001b0| 75 6e 63 74 69 6f 6e 73 | 20 28 43 75 73 74 6f 6d |unctions| (Custom|
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|000001d0| 20 76 61 72 69 61 62 6c | 65 73 20 6f 74 68 65 72 | variabl|es other|
|000001e0| 20 74 68 61 6e 20 74 68 | 6f 73 65 20 69 6e 20 74 | than th|ose in t|
|000001f0| 68 65 20 46 75 6e 63 74 | 69 6f 6e 20 61 72 67 75 |he Funct|ion argu|
|00000200| 6d 65 6e 74 2e 0d 0d 41 | 20 74 79 70 69 63 61 6c |ment...A| typical|
|00000210| 20 72 65 66 65 72 65 6e | 63 65 20 74 6f 20 22 46 | referen|ce to "F|
|00000220| 75 6e 22 20 69 73 3a 0d | 0d 41 3d 33 2b 46 75 6e |un" is:.|.A=3+Fun|
|00000230| 28 32 3b 34 29 2d 42 20 | 0d 0d 49 66 20 46 75 6e |(2;4)-B |..If Fun|
|00000240| 28 78 3b 79 29 20 69 73 | 20 64 65 66 69 6e 65 64 |(x;y) is| defined|
|00000250| 20 6f 6e 20 61 20 46 75 | 6e 63 74 69 6f 6e 20 53 | on a Fu|nction S|
|00000260| 6c 61 74 65 20 61 73 20 | 46 75 6e 28 78 3b 79 29 |late as |Fun(x;y)|
|00000270| 20 3d 20 78 5e 32 2b 79 | 20 20 74 68 65 6e 20 50 | = x^2+y|  then P|
|00000280| 6f 77 65 72 4d 61 74 68 | 20 73 75 62 73 74 69 74 |owerMath| substit|
|00000290| 75 74 65 73 20 32 20 66 | 6f 72 20 78 20 61 6e 64 |utes 2 f|or x and|
|000002a0| 20 34 20 66 6f 72 20 79 | 2e 20 20 54 68 65 20 65 | 4 for y|.  The e|
|000002b0| 78 70 72 65 73 73 69 6f | 6e 20 6f 6e 20 74 68 65 |xpressio|n on the|
|000002c0| 20 50 72 6f 62 6c 65 6d | 20 53 6c 61 74 65 20 62 | Problem| Slate b|
|000002d0| 65 63 6f 6d 65 73 20 20 | 41 20 3d 20 33 2b 28 32 |ecomes  |A = 3+(2|
|000002e0| 5e 32 2b 34 29 2d 42 0d | 0d 43 75 73 74 6f 6d 20 |^2+4)-B.|.Custom |
|000002f0| 43 61 6c 63 75 6c 75 73 | 20 46 75 6e 63 74 69 6f |Calculus| Functio|
|00000300| 6e 73 0d 0d 41 20 76 65 | 72 79 20 69 6d 70 6f 72 |ns..A ve|ry impor|
|00000310| 74 61 6e 74 20 66 65 61 | 74 75 72 65 20 69 73 20 |tant fea|ture is |
|00000320| 74 68 65 20 61 62 69 6c | 69 74 79 20 74 6f 20 64 |the abil|ity to d|
|00000330| 65 66 69 6e 65 20 43 61 | 6c 63 75 6c 75 73 20 46 |efine Ca|lculus F|
|00000340| 75 6e 63 74 69 6f 6e 73 | 2e 20 09 0d 50 6f 77 65 |unctions|. ..Powe|
|00000350| 72 4d 61 74 68 20 72 65 | 63 6f 67 6e 69 7a 65 73 |rMath re|cognizes|
|00000360| 20 63 75 73 74 6f 6d 2d | 62 75 69 6c 74 20 44 69 | custom-|built Di|
|00000370| 66 66 65 72 65 6e 74 69 | 61 6c 20 61 6e 64 20 49 |fferenti|al and I|
|00000380| 6e 74 65 67 72 61 6c 20 | 46 75 6e 63 74 69 6f 6e |ntegral |Function|
|00000390| 73 2e 20 20 41 20 74 79 | 70 69 63 61 6c 20 63 75 |s.  A ty|pical cu|
|000003a0| 73 74 6f 6d 2d 62 75 69 | 6c 74 20 44 69 66 66 65 |stom-bui|lt Diffe|
|000003b0| 72 65 6e 74 69 61 6c 20 | 46 75 6e 63 74 69 6f 6e |rential |Function|
|000003c0| 20 69 73 3a 0d 0d b6 28 | 43 4f 53 28 55 29 3b 58 | is:...(|COS(U);X|
|000003d0| 29 20 3d 20 53 49 4e 28 | 55 29 2a b6 28 55 3b 58 |) = SIN(|U)*.(U;X|
|000003e0| 29 0d 0d 54 68 69 73 20 | 66 65 61 74 75 72 65 20 |)..This |feature |
|000003f0| 61 6c 6c 6f 77 73 20 76 | 69 72 74 75 61 6c 6c 79 |allows v|irtually|
|00000400| 20 6f 70 65 6e 20 65 6e | 64 65 64 20 43 61 6c 63 | open en|ded Calc|
|00000410| 75 6c 75 73 20 6f 70 65 | 72 61 74 69 6f 6e 73 2e |ulus ope|rations.|
|00000420| 20 57 68 65 6e 20 64 65 | 66 69 6e 69 6e 67 20 63 | When de|fining c|
|00000430| 75 73 74 6f 6d 20 69 6e | 74 65 67 72 61 6c 73 2c |ustom in|tegrals,|
|00000440| 20 62 65 20 73 75 72 65 | 20 74 68 61 74 20 74 68 | be sure| that th|
|00000450| 65 20 64 65 72 69 76 61 | 74 69 76 65 20 69 73 20 |e deriva|tive is |
|00000460| 61 6c 73 6f 20 64 65 66 | 69 6e 65 64 20 62 65 63 |also def|ined bec|
|00000470| 61 75 73 65 20 50 6f 77 | 65 72 4d 61 74 68 20 75 |ause Pow|erMath u|
|00000480| 73 65 64 20 74 68 65 20 | 64 65 72 69 76 61 74 69 |sed the |derivati|
|00000490| 76 65 20 74 6f 20 64 65 | 74 65 72 6d 69 6e 65 20 |ve to de|termine |
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|000004c0| 6e 2e 0d 0d 54 65 73 74 | 20 79 6f 75 72 20 43 75 |n...Test| your Cu|
|000004d0| 73 74 6f 6d 20 46 75 6e | 63 74 69 6f 6e 73 20 62 |stom Fun|ctions b|
|000004e0| 65 66 6f 72 65 20 75 73 | 69 6e 67 20 74 68 65 6d |efore us|ing them|
|000004f0| 20 69 6e 20 61 20 70 72 | 6f 62 6c 65 6d 2e 20 42 | in a pr|oblem. B|
|00000500| 65 20 73 75 72 65 20 74 | 68 61 74 20 79 6f 75 72 |e sure t|hat your|
|00000510| 20 43 61 6e 6f 6e 69 63 | 61 6c 20 46 75 6e 63 74 | Canonic|al Funct|
|00000520| 69 6f 6e 20 61 72 67 75 | 6d 65 6e 74 73 20 6f 6e |ion argu|ments on|
|00000530| 20 74 68 65 20 46 75 6e | 63 74 69 6f 6e 20 53 6c | the Fun|ction Sl|
|00000540| 61 74 65 20 20 22 6d 61 | 74 63 68 75 70 22 20 77 |ate  "ma|tchup" w|
|00000550| 69 74 68 20 72 65 66 65 | 72 65 6e 63 65 73 20 66 |ith refe|rences f|
|00000560| 72 6f 6d 20 74 68 65 20 | 50 72 6f 62 6c 65 6d 20 |rom the |Problem |
|00000570| 53 6c 61 74 65 2e 0d 0d | 42 65 20 70 61 72 74 69 |Slate...|Be parti|
|00000580| 63 75 6c 61 72 6c 79 20 | 63 61 72 65 66 75 6c 20 |cularly |careful |
|00000590| 74 68 61 74 20 79 6f 75 | 20 65 6d 70 6c 6f 79 20 |that you| employ |
|000005a0| 63 6f 72 72 65 63 74 20 | 43 61 6c 63 75 6c 75 73 |correct |Calculus|
|000005b0| 20 72 75 6c 65 73 20 77 | 68 65 6e 20 63 72 65 61 | rules w|hen crea|
|000005c0| 74 69 6e 67 20 43 75 73 | 74 6f 6d 20 43 61 6c 63 |ting Cus|tom Calc|
|000005d0| 75 6c 75 73 20 46 75 6e | 63 74 69 6f 6e 73 2e 20 |ulus Fun|ctions. |
|000005e0| 20 50 6f 77 65 72 4d 61 | 74 68 20 69 73 20 6e 6f | PowerMa|th is no|
|000005f0| 74 20 67 75 61 72 61 6e | 74 65 65 64 20 74 6f 20 |t guaran|teed to |
|00000600| 68 61 6e 64 6c 65 20 65 | 76 65 72 79 20 49 6e 74 |handle e|very Int|
|00000610| 65 67 72 61 6c 2e 0d 0d | 0d 0d 00 00 00 00 00 00 |egral...|........|
|00000620| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000630| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000640| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000650| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000660| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000670| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000680| 00 00 01 00 00 00 02 74 | 00 00 01 74 00 00 00 3e |.......t|...t...>|
|00000690| 00 00 00 01 00 02 00 00 | 00 48 00 50 00 00 00 00 |........|.H.P....|
|000006a0| 02 f0 02 80 ff dc ff ec | 02 f4 02 94 01 02 05 28 |........|.......(|
|000006b0| 10 43 75 73 74 6f 6d 20 | 46 75 6e 63 74 69 6f 6e |.Custom |Function|
|000006c0| 73 63 02 00 00 00 54 45 | 58 54 4d 41 43 41 01 00 |sc....TE|XTMACA..|
|000006d0| 00 00 54 45 58 54 4d 41 | 43 41 01 00 ff fa 00 bc |..TEXTMA|CA......|
|000006e0| 02 19 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000006f0| 00 00 99 a1 30 18 00 00 | 05 9a 00 00 02 b2 00 00 |....0...|........|
|00000700| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 19 00 df |........|........|
|00000710| 00 19 00 df fe 52 00 12 | ff f2 00 1e ff f2 00 ec |.....R..|........|
|00000720| ff f2 01 ba ff ff ff ff | ff 00 0c 00 00 01 00 01 |........|........|
|00000730| 00 00 00 01 00 00 00 00 | 00 00 ff f2 00 1e ff f2 |........|........|
|00000740| 00 ec ff f2 01 ba ff ff | ff ff ff 00 0c 00 00 01 |........|........|
|00000750| 00 01 00 00 00 01 00 00 | 00 00 00 00 ff f2 00 1e |........|........|
|00000760| ff f2 00 ec ff f2 01 ba | ff ff ff ff ff 00 0c 00 |........|........|
|00000770| 00 01 00 00 00 00 00 00 | cf 52 00 10 00 00 00 00 |........|.R......|
|00000780| 00 00 00 20 2e 2c 3b 24 | 00 00 d0 00 00 2f ff 60 |... .,;$|...../.`|
|00000790| 20 41 4d 00 20 50 4d 00 | 3a 00 00 00 00 00 00 00 | AM. PM.|:.......|
|000007a0| 00 00 00 01 00 00 01 4c | 06 53 75 6e 64 61 79 00 |.......L|.Sunday.|
|000007b0| 00 00 00 00 00 00 00 00 | 06 4d 6f 6e 64 61 79 00 |........|.Monday.|
|000007c0| 00 00 00 00 00 00 00 00 | 07 54 75 65 73 64 61 79 |........|.Tuesday|
|000007d0| 00 00 00 00 00 00 00 00 | 09 57 65 64 6e 65 73 64 |........|.Wednesd|
|000007e0| 61 79 00 00 00 00 00 00 | 08 54 68 75 72 73 64 61 |ay......|.Thursda|
|000007f0| 79 00 00 00 00 00 00 00 | 06 46 72 69 64 61 79 00 |y.......|.Friday.|
|00000800| 00 00 00 00 00 00 00 00 | 08 53 61 74 75 72 64 61 |........|.Saturda|
|00000810| 79 00 00 00 00 00 00 00 | 07 4a 61 6e 75 61 72 79 |y.......|.January|
|00000820| 00 00 00 00 00 00 00 00 | 08 46 65 62 72 75 61 72 |........|.Februar|
|00000830| 79 00 00 00 00 00 00 00 | 05 4d 61 72 63 68 00 00 |y.......|.March..|
|00000840| 00 00 00 00 00 00 00 00 | 05 41 70 72 69 6c 00 00 |........|.April..|
|00000850| 00 00 00 00 00 00 00 00 | 03 4d 61 79 00 00 00 00 |........|.May....|
|00000860| 00 00 00 00 00 00 00 00 | 04 4a 75 6e 65 00 00 00 |........|.June...|
|00000870| 00 00 00 00 00 00 00 00 | 04 4a 75 6c 79 00 00 00 |........|.July...|
|00000880| 00 00 00 00 00 00 00 00 | 06 41 75 67 75 73 74 00 |........|.August.|
|00000890| 00 00 00 00 00 00 00 00 | 09 53 65 70 74 65 6d 62 |........|.Septemb|
|000008a0| 65 72 00 00 00 00 00 00 | 07 4f 63 74 6f 62 65 72 |er......|.October|
|000008b0| 00 00 00 00 00 00 00 00 | 08 4e 6f 76 65 6d 62 65 |........|.Novembe|
|000008c0| 72 00 00 00 00 00 00 00 | 08 44 65 63 65 6d 62 65 |r.......|.Decembe|
|000008d0| 72 00 00 00 00 00 00 00 | ff ff 00 03 00 00 00 00 |r.......|........|
|000008e0| 2c 20 00 00 20 00 00 00 | 2c 20 00 00 00 00 00 00 |, .. ...|, ......|
|000008f0| 00 01 4e 75 00 00 01 00 | 00 00 02 74 00 00 01 74 |..Nu....|...t...t|
|00000900| 00 00 00 3e 00 00 4f 1c | 00 7a 00 00 00 1c 00 3e |...>..O.|.z.....>|
|00000910| 00 00 49 4e 54 4c 00 01 | 00 0a 00 01 ff ff 20 00 |..INTL..|...... .|
|00000920| 00 24 00 00 cf 56 00 00 | ff ff 20 00 00 00 00 00 |.$...V..|.. .....|
|00000930| cf 6a 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.j......|........|
|00000940| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000950| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000960| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000970| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+