~v200 200 ~w38 0 518 784 0 360 0 83 ~f? 14 12 10
? 3 0 1 0 ? ? ? "Arial" ? ? ? 1 ? 0 1
"Times" 12 ? ? 8 0 c n 109 1 0 0 k 468
i"?n             page ?p?a"
-2 1 26177 26178 26115 26178 1 1 1 1 0 0
8405120 0 -1 0 1 -1 -1 -1 -1 -1 0 1 ? ? 
~Q
]|Expr|[#b @`bb#_b#_b#_})%# b'4" *|: ;bP8&c0!*Finite Taylor Series|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?f0 (Taylor)~p1
1 ~Ht(Taylor(?y,?x)):(Summation(k):(0):(n-1)*(EvaluateAt((Diff(~
 x))^k*?y):(x=?x))/k!*(x-?x)^k)~p0
2 ~V?f0 (f)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP8&c0!*Declarations|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Trigonometry|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
2 ~V?c1 ('p)~p0
3 ~V?f256 (sin)~p0
3 ~V?f257 (cos)~p0
3 ~V?f258 (tan)~p0
3 ~V?f261 (sec)~p0
3 ~V?f260 (csc)~p0
3 ~V?f262 (cot)~p0
3 ~V?f272 (arcsin)~p0
3 ~V?f273 (arccos)~p0
3 ~V?f274 (arctan)~p0
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Hyperbolic|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
2 ~V?f293 (sech)~p0
3 ~V?f288 (sinh)~p0
3 ~V?f289 (cosh)~p0
3 ~V?f290 (tanh)~p0
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
2 ~V?f32 (log)~p0
3 ~V?f307 (ln)~p0
3 ~V?f291 (exp)~p0
3 ~V?c2 (e)~p0
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Standard Rules|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
2 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
3 ~Ht(?x^(-?y)):(1/?x^?y)~p0
4 ~Hs(exp(?z)):(e^?z)~p0
4 ~Hs(e^(ln(?x))):(?x)~p0
4 ~Hs(10^(log(?x))):(?x)~p0
4 ~Hs(?y^(log_?y(?x))):(?x)~p0
4 ~Hs(ln(e^?x)):(?x)~p0
4 ~Hs(log(10^?x)):(?x)~p0
4 ~Hs(log_?y(?y^?x)):(?x)~p0
4 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0
4 ~He(log(?u*?v)):(log(?u)+log(?v))~p0
4 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0
4 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0
4 ~He(log(?u/?v)):(log(?u)-log(?v))~p0
4 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0
4 ~He(ln(?u^?v)):(?v*ln(?u))~p0
4 ~He(log(?u^?v)):(?v*log(?u))~p0
4 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0
4 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0
4 ~He(log(sqrt(?u))):(1/2*log(?u))~p0
4 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0
4 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Trigonometry|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP8&c0!*Simplify ,M negation|
  | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Hs(sin(-?x)):(-sin(?x))~p0
5 ~Hs(cos(-?x)):(cos(?x))~p0
5 ~Hs(tan(-?x)):(-tan(?x))~p0
5 ~Hs(sin('p)):(0)~p0
5 ~Hs(sin(?n*'p)):(0)~p0
5 ~Hs(cos(1/2*'p)):(0)~p0
5 ~Hs(cos(?n/2*'p)):(0)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP8&c0!*Transform to basic|
  | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0
5 ~Ht(csc(?x)):(1/(sin(?x)))~p0
5 ~Ht(sin(?x)):(1/(csc(?x)))~p0
5 ~Ht(sec(?x)):(1/(cos(?x)))~p0
5 ~Ht(cos(?x)):(1/(sec(?x)))~p0
5 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Trig Addition|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0
5 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0
5 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0
5 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0
5 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*sin((?n-1)*?x))~p0
5 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*sin((?n-1)*?x))~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})/# b$L" *|: ;bP8&c0!*Transform ,M into|
  | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0
5 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0
5 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0
5 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0
5 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0
5 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0
5 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})b @# b%4" *|: ;bP8&c0!*substituting |
  |z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H|
  |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0
5 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Other rules|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0
5 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0
5 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0
5 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0
5 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b!T" *|: ;bP8&c0!*Hyperbolic|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP8&c0!*Simplify ,M negation|
  | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Hs(sinh(-?x)):(-sinh(?x))~p0
5 ~Hs(cosh(-?x)):(cosh(?x))~p0
5 ~Hs(tanh(-?x)):(-tanh(?x))~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP8&c0!*Transform into |
  |other types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht((sinh(?x))^2):((cosh(?x))^2-1)~p0
5 ~Ht((cosh(?x))^2):(1+(sinh(?x))^2)~p0
5 ~Ht((tanh(?x))^2):(1-(sech(?x))^2)~p0
5 ~Ht(sinh(?x)):((e^?x-e^(-?x))/2)~p0
5 ~Ht(cosh(?x)):((e^?x+e^(-?x))/2)~p0
5 ~Ht(tanh(?x)):((e^?x-e^(-?x))/(e^?x+e^(-?x)))~p0
5 ~Ht(tanh(?x)):((sinh(?x))/(cosh(?x)))~p0
5 ~Hs((cosh(?x))^2-(sinh(?x))^2):(1)~p0
5 ~Hs(-(cosh(?x))^2+(sinh(?x))^2):(-1)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Other hyperbolic|
  | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0
5 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0
5 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0
5 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Integration Rules|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
3 ~Q
]|Expr|[#b @`bb#_b#_b#_}))# b$8" *|: ;bP8&c0!*after Partial Fraction|
  | Decomposition integration}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Hs(ln(?x+?b*i)):((-i*arctan(?x/?b)+1/2*ln(?x^2+?b^2))+1/2*'p*~
 i)~p0
5 ~Hs(ln(?x+i)):((-i*arctan(?x)+1/2*ln(?x^2+1))+1/2*'p*i)~p0
5 ~Hs(ln(?x-?b*i)):((i*arctan(?x/?b)+1/2*ln(?x^2+?b^2))+1/2*'p*~
 i)~p0
5 ~Hs(ln(?x-i)):((i*arctan(?x)+1/2*ln(?x^2+1))+1/2*'p*i)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$4" *|: ;bP8&c0!*Derivatives of |
  |Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
4 ~Ht(Diff(?x)*(Integral(?y*d*?x))):(?y)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b'4" *|: ;bP8&c0!*Standard Names|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
2 ~V?c4 (i)~p0
3 ~V?d16 (d)~p0
3 ~V?v0 (k)~p0
3 ~V?c0 (n)~p0
3 ~V?c0 (c)~p0
3 ~V?c0 (a)~p0
3 ~V?c0 (b)~p0
3 ~V?v0 (z)~p0
3 ~V?v0 (y)~p0
3 ~V?v0 (x)~p0
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4" *|: ;bP8&c0!*Input|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"0" *|: ;bP8&c0!*function|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
1 ~A(f(x)=sin('p*x))~p0
255 ~A(f(?x)=sin('p*?x))~p0
2 ~d~sb/_!!   }
b00&!  c#T"_c/__c/__!"}
^ _~A(x=?x)~p0
255 ~A(y=f(x))~p0
2 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})## b"0" *|: ;bP8&c0!*expansion point|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A(x_0=1)~p0
255 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"0["! )%# b"0" *|: ;bP8&c0!*number|
  | of terms}& b!( b"0 b#8 b$@ b%H b&P!WW})%# b"0,Hincluding vanished|
  |,I}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A(n=6)~p0
255 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4" *|: ;bP8&c0!*Output|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(y_n=Taylor(f(x),x_0))~p1
1 ~A(y_n=Taylor(sin('p*x),x_0))~p0
2 ~sb/_!!   }
b00,!  c#T"!c#L"!c&T# c#L"_c/__c/__!"}
^ _~A(y_n=~
 Summation(k):(0):(n-1)*((-x_0+x)^k*(EvaluateAt((Diff(x))^k*sin(~
 'p*x)):(x=x_0)))/k!)~p0
3 ~sb/_!!   }
#'!  c#T"!c#L"_c/__c/__!}
^ _~A(y_n='p*(-x_0+x)*cos(~
 'p*x_0)+sin('p*x_0)+1/120*(-x_0+x)^5*(EvaluateAt((Diff(x))^5*~
 sin('p*x)):(x=x_0))+1/24*(-x_0+x)^4*(EvaluateAt((Diff(x))^4*sin(~
 'p*x)):(x=x_0))+1/6*(-x_0+x)^3*(EvaluateAt((Diff(x))^3*sin('p*~
 x)):(x=x_0))+1/2*(-x_0+x)^2*(EvaluateAt((Diff(x))^2*sin('p*x)):(~
 x=x_0)))~p0
4 ~sb/_!!   }
"&!  c#T"!c"H"_c/__c/__}
^ _~A(y_n=-1/120*'p^5*x_~
 0^5*cos('p*x_0)+1/24*'p^5*x*x_0^4*cos('p*x_0)+1/6*'p^3*x_0^3*~
 cos('p*x_0)-1/12*'p^5*x^2*x_0^3*cos('p*x_0)+1/12*'p^5*x^3*x_0^~
 2*cos('p*x_0)-1/2*'p^3*x*x_0^2*cos('p*x_0)-'p*x_0*cos('p*x_0)-~
 1/24*'p^5*x^4*x_0*cos('p*x_0)+1/2*'p^3*x^2*x_0*cos('p*x_0)+1/~
 120*'p^5*x^5*cos('p*x_0)-1/6*'p^3*x^3*cos('p*x_0)+'p*x*cos('p*~
 x_0)+sin('p*x_0)+1/24*'p^4*x_0^4*sin('p*x_0)-1/6*'p^4*x*x_0^3*~
 sin('p*x_0)-1/2*'p^2*x_0^2*sin('p*x_0)+1/4*'p^4*x^2*x_0^2*sin(~
 'p*x_0)-1/6*'p^4*x^3*x_0*sin('p*x_0)+'p^2*x*x_0*sin('p*x_0)+1/~
 24*'p^4*x^4*sin('p*x_0)-1/2*'p^2*x^2*sin('p*x_0))~p0
5 ~sb/_!!   }
"&!  c#T"!c"L&_c/__c/__}
^ _~A(y_n=-2.5501640398773451*~
 x^5+12.750820199386725*x^4-20.333927618723482*x^3+9.9985020586235436*~
 x^2-0.38927451282661074*x+0.52404391341716883)~p0
1 ~d~sb/_!!   }
$&!  c#T"!c"L5_c/__c/__}
^ _~G1 1 336 484
1 1 3 4 10
(~
 -0.5...2.5):(-1.5000000000000002...1.5):(?=0...2*'p):('p/5):(~
 10)~Q
]|Expr|[#b @`bb#_b#_b#_})!# b#8" *|: ;bP8&c0!*Declarations|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~R8405120 ? (x,y):(y=bottom...top):(x=left...right):(0)~p0
1 ~gc1 2 ? 0 -2731 -4096 0
65535 -2731 4096 0
~gc1 2 ? 0 0 -4096 0
65535 0 4096 0
~gc1 2 ? 0 2731 -4096 0
65535 2731 4096 0
~
 ~R8405120 ? (x,y):(x=left...right):(y=bottom...top):(0)~p0
1 ~gc1 2 ? 0 -4096 -2731 0
65535 4096 -2731 0
~gc1 2 ? 0 -4096 0 0
65535 4096 0 0
~gc1 2 ? 0 -4096 2731 0
65535 4096 2731 0
~
 ~X2 8405120 (left,y):(y=bottom...top):(y)~p0
1 ~gc1 2 ? 0 -4096 -4096 0
65535 -4096 4096 0
~X1 8405120 (x,bottom):(~
 x=left...right):(x)~p0
1 ~gc1 2 ? 0 -4096 -4096 0
65535 4096 -4096 0
~V?c64 (left)~p0
1 ~V?c65 (right)~p0
1 ~V?c66 (bottom)~p0
1 ~V?c67 (top)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b#8" *|: ;bP8&c0!*function|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 16711680 ? (x,y):(x=left...right)~p0
1 ~gc0 47 ? 0 -4096 -2731 0
1486 -3910 -2669 0
2378 -3799 -2573 0
3071 -3712 -2469 0
4228 -3567 -2241 0
6342 -3303 -1671 0
8192 -3072 -1045 0
12684 -2510 684 0
15062 -2213 1531 0
16912 -1982 2072 0
18233 -1817 2370 0
19026 -1718 2509 0
19719 -1631 2604 0
20876 -1486 2704 0
21432 -1417 2726 0
21767 -1375 2730 0
22324 -1305 2724 0
23254 -1189 2675 0
24575 -1024 2523 0
25368 -925 2388 0
26259 -814 2199 0
27746 -628 1805 0
29596 -396 1203 0
35938 396 -1202 0
38052 661 -1881 0
39538 846 -2258 0
40430 958 -2436 0
41123 1044 -2547 0
41574 1101 -2605 0
41846 1135 -2635 0
42008 1155 -2651 0
42280 1189 -2675 0
43072 1288 -2720 0
44394 1453 -2717 0
45087 1540 -2676 0
46244 1685 -2549 0
48622 1982 -2072 0
50736 2246 -1445 0
53114 2543 -584 0
54964 2775 138 0
57078 3039 948 0
58928 3270 1588 0
61306 3567 2241 0
62462 3712 2468 0
63156 3799 2572 0
64048 3910 2668 0
65535 4096 2731 0
~
 ~S17 ? 16711680 ? ? (x_0,f(x_0)):(?):(8)~p0
1 ~gc-1 1 ? 0 0 0 0
~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b#8" *|: ;bP8&c0!*Taylor series|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 255 ? (x,y_n):(x=left...right)~p0
1 ~gc0 79 ? 0 -32768 -32768 0
1189 -32768 -32768 0
1486 -32768 -32768 0
1634 -32768 -32768 0
1643 -32768 -32768 0
1647 -3890 12283 0
1652 -3889 12268 0
1671 -3887 12211 0
1689 -3885 12157 0
1708 -3882 12100 0
1783 -3873 11877 0
2378 -3799 10225 0
4228 -3567 6245 0
6342 -3303 3436 0
7498 -3159 2504 0
8192 -3072 2108 0
8748 -3002 1866 0
9083 -2961 1749 0
9640 -2891 1599 0
10221 -2818 1495 0
10570 -2775 1455 0
11065 -2713 1425 0
11362 -2676 1420 0
11857 -2614 1431 0
12167 -2575 1449 0
12684 -2510 1495 0
15062 -2213 1875 0
16912 -1982 2234 0
19026 -1718 2570 0
20182 -1573 2686 0
20876 -1486 2726 0
21432 -1417 2742 0
21767 -1375 2743 0
22696 -1259 2717 0
23254 -1189 2680 0
24046 -1090 2598 0
25368 -925 2388 0
27746 -628 1805 0
29596 -396 1203 0
35938 396 -1202 0
38052 661 -1881 0
39538 846 -2259 0
40430 958 -2437 0
41123 1044 -2549 0
41846 1135 -2639 0
42280 1189 -2679 0
43072 1288 -2728 0
43898 1391 -2744 0
44394 1453 -2736 0
44827 1507 -2719 0
45087 1540 -2704 0
45520 1594 -2673 0
46244 1685 -2601 0
48622 1982 -2234 0
50736 2246 -1825 0
52222 2432 -1574 0
53114 2543 -1469 0
53807 2630 -1426 0
54240 2684 -1421 0
54692 2741 -1435 0
54964 2775 -1455 0
55459 2836 -1516 0
55756 2874 -1570 0
56251 2935 -1689 0
57078 3039 -1984 0
58928 3270 -3190 0
61306 3567 -6243 0
63156 3799 -10223 0
63750 3873 -11871 0
63824 3882 -12091 0
63842 3884 -12145 0
63861 3887 -12202 0
63879 3889 -12256 0
63888 3890 -12283 0
63893 -32768 -32768 0
63898 -32768 -32768 0
64047 -32768 -32768 0
64345 -32768 -32768 0
65535 -32768 -32768 0
~t~p0
0 ~c2
130 -1 129 -1 131 -1 ~c2
139 -1 138 -1 129 -1 ~c2
140 -1 139 -1 2 -1 ~c3
141 -1 140 -1 136 -1 120 -1 ~c1
142 -1 141 -1 ~c3
143 -1 142 -1 134 -1 126 -1 ~e