~v350 200 zw#^g]inZi`bVVYYc[Dccb`bZD[Y wx$N_edVQU\VYWlPQU`TOU`TWWTVaWlXS ~w169 8 565 818 0 0 0 0 ~f? 18 15 12 ? 2 1 0 0 ? ? ? "Buchdrucker" ? ? ? 0 ? 1 1 "Times" 12 ? ? 5 0 c n 1 1 0 0 k 468 f"?n page ?p?a" ? 0 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 1 0 -1 -1 -1 -1 -1 1 1 0 0 2 0 ? ? ? ? ? ? ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4`fb#_}" *^: ;bP8&c0!*`g| |1''| |b#(-___| |3b6,b1N| |M,6r;%14!\!!!!.8Ou6I!!!#?!!!!.#Qau+!+R+Zc2[hI2+^2%<-Xr#=A<]!| |2@poEh$2gA!q68GjT??#Z;7S9f[9pCqZ?W)5[sTlP'_`%\j/Y,#I"<4$dm#r| |bTcA'>td]V8WMil`U0Dr5R?G4r:i4@)%*$*M_i..'itl['@TAfs^sFcW$0&)XJ2^BgNUBS<:VC(1QRDsel#_fW8m*2QWL0h"sejR&2\;b1^k#tIe88c| |\\c,<@9>.KH4fW*e^]rN]'pee6NEM"kGDtEbW\Yg^i9$Bdo7og4+<8Z#Mtc!| |Ei"%=H+2NkO[f_3&Mj"h_!)b6Hi!o`:5H*U38k_q]WhOMs| |4@`*Y6D-\nH$MF0l"\'32^1uFom0mWY#_SW$p!L(O?ChiJ.Rm@.39X)Nf]pY| |Lna+liP@?F`n5WUKl\;i@2O`4$W2NRVJ33bCEWfbG,R$O`Sq/KYLaFS"@8\s| |QicQd)W_7OTVcGW,l&YR:%tPo4B>%e$8JJ'g&piYEd[.Ppo#L?;@gI_AF`OV| |8i*b(]=>AL:#Q$M??Pd#%n"G0]a?Jp[4I4IK!@!dJp4S+;Tere%fk6Uhsl=E| |H@-`%Og6B]UgFMmCXI6,QDaq4n;^95+Lqj9O[Qm?C+IH49Ejm2/XjoGHfF3I| |)5-NOi2r\T!:WKYV)5s_]A]lc=J"^7NsU#oXo=(]XO9!(fUS7'8ja| |JcGcN| |9}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b$L" *^: ;bP7&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f276 (arccsc)~p0 3 ~V?f278 (arccot)~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 ~V?f277 (arcsec)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b$L" *^: ;bP7&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f309 (arcsech)~p0 3 ~V?f304 (arcsinh)~p0 3 ~V?f294 (coth)~p0 3 ~V?f310 (arccoth)~p0 3 ~V?f306 (arctanh)~p0 3 ~V?f293 (sech)~p0 3 ~V?f288 (sinh)~p0 3 ~V?f289 (cosh)~p0 3 ~V?f290 (tanh)~p0 3 ~V?f305 (arccosh)~p0 3 ~V?f308 (arccsch)~p0 3 ~V?f292 (csch)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})%# b$L" *^: ;bP7&c0!*Logarithms | |,F Powers}& b!( b"0 b#8 b$@ 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#_}`f#})## b$L" *^: ;bP7&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})%# b$L" *^: ;bP7&c0!*Logarithms | |,F Powers}& b!( b"0 b#8 b$@ 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 ~He(?z^(?x+?y)):(?z^?x*?z^?y)~p0 4 ~He(?z^(?x-?y)):(?z^?x*?z^(-?y))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b$L" *^: ;bP7&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})+# b$L" *^: ;bP7&c0!*Simplify ,M| | negation and common zeros}& b!( b"0 b#8 b$@ 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 ~Hs(-(cos(?x))^2-(sin(?x))^2):(-1)~p0 5 ~Hs(cos('p/2)):(0)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})'# b$L" *^: ;bP7&c0!*Transform to| | basic types}& b!( b"0 b#8 b$@ 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#_}`f#})## b$L" *^: ;bP7&c0!*Trig Addition| |}& b!( b"0 b#8 b$@ 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#_}`f#})/# b$L" *^: ;bP7&c0!*Transform ,M| | into another flavor of trig function}& b!( b"0 b#8 b$@ 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#_}`f#})b @# b%4" *^: ;bP7&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$@ b%H b&P!WW}]|[~p1 4 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 5 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})## b$L" *^: ;bP7&c0!*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 5 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 5 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 5 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 5 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b!T" *^: ;bP7&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})+# b$L" *^: ;bP7&c0!*Simplify ,M| | negation and common zeros}& b!( b"0 b#8 b$@ 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#_}`f#})'# b$L" *^: ;bP7&c0!*Transform into| | other types}& b!( b"0 b#8 b$@ 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#_}`f#})%# b$L" *^: ;bP7&c0!*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ 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#_}`f#})!# b'4" *^: ;bP7&c0!*Constants| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?c0 (C)~p0 3 ~V?c5 ('o)~p0 3 ~V?c1 ('p)~p0 3 ~V?c0 (c)~p0 3 ~V?c0 (b)~p0 3 ~V?c0 (a)~p0 3 ~V?c4 (i)~p0 3 ~V?c3 ('N)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b'4" *^: ;bP7&c0!*Variables| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?v0 (n)~p0 3 ~V?v0 (h)~p0 3 ~V?v0 (v)~p0 3 ~V?v0 (u)~p0 3 ~V?v0 (w)~p0 3 ~V?v0 ('f)~p0 3 ~V?v0 ('r)~p0 3 ~V?v0 ('q)~p0 3 ~V?v0 (r)~p0 3 ~V?v0 (t)~p0 3 ~V?v0 (z)~p0 3 ~V?v0 (y)~p0 3 ~V?v0 (x)~p0 3 ~V?v0 (k)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b'4" *^: ;bP7&c0!*Functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f162 (max)~p0 3 ~V?f161 (min)~p0 3 ~V?f132 (FromSpherical)~p0 3 ~V?f130 (FromCylindrical)~p0 3 ~V?f128 (FromPolar)~p0 3 ~V?f144 (RowsOf)~p0 3 ~V?f146 (ColsOf)~p0 3 ~V?d16 (d)~p0 2 ~He((?a^?b)^?c):(?a^(?b*?c))~p0 1 ~He(?a*?a^?b):(?a^(1+?b))~p0 1 ~He(?a^?b*?a^?c):(?a^(?b+?c))~p0 1 ~He(?a^?b*?a^(-?c)):(?a^(?b-?c))~p0 1 ~He((-?a^?b)/?a^?c):(-?a^?b/?a^?c)~p0 1 ~Ht((?a/?b)^?c):(?a^?c/?b^?c)~p0 1 ~He((?a^?b/?c^?d)/(?e^?f/?g^?h)):(?a^?b/?e^?f*~ ?g^?h/?c^?d)~p0 1 ~He(?a^(-?b)*?c^?d):(?c^?d/?a^?b)~p0 1 ~He(?a^?b*1/?c^?d):(?a^?b/?c^?d)~p0 1 ~Ht((?a*?b*?c)^?d):(?a^?d*?b^?d*?c^?d)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})(# b'4" *^: ;bP:&c0!)Vereinfache| |,L berechne den Termwert}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~He(?a^?b/?a^?c):(?a^(?b-?c))~p0 1 ~He(?a/?b*?c/?d):(?a/?d*?c/?b)~p0 1 ~He((?a*?b)/(?c*?d)):((?a*?b)/(?d*?c))~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})"# b'4" *^: ;bP8&c0!*1,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A((3/4)^2)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})"# b'4" *^: ;bP8&c0!*2,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A((4/5^2)^3)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})"# b'4" *^: ;bP8&c0!*3,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A((3^5/7^2)^2*(7^2/3^3)^3)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 1 ~A((3^5/7^2)^2*(7^2/3^3)^3=3^1*7^(6-4))~p0 2 ~sb/_! } !* c#T"!c"H" c%X"!c"L"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=3^(10-9)*7^6/7^4)~p0 2 ~sb/_! } %( c#T"!c"H" c"\"_c/__c/__} ^ _~A(~ (3^5/7^2)^2*(7^2/3^3)^3=3^10/7^(2*2)*7^(2*3)/3^~ (3*3))~p0 2 ~sb/_! } !, c#T"!c"H" c"\" c%X"!c"H"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=3^10/7^(2*2)*7^6/3^~ (3*3))~p0 3 ~sb/_! } !, c#T"!c"H"!c"\" c%X"!c"H"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=3^10/7^4*7^6/3^(3*3))~p0 4 ~sb/_! } !, c#T"!c"H" c"\"!c%X"!c"H"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=3^(5*2)/(7^2)^2*(7^~ 2)^3/(3^3)^3)~p0 2 ~sb/_! } %* c#T"!c"H" c"\" c%X"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=3^(5*2)/(7^2)^2*7^(~ 2*3)/(3^3)^3)~p0 3 ~sb/_! } %* c#T"!c"H"!c"\" c%X"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=3^(5*2)/7^(2*2)*7^(~ 2*3)/(3^3)^3)~p0 4 ~sb/_! } %* c#T"!c"H" c"\"!c%X"_c/__c/__} ^ _~ ~A((3^5/7^2)^2*(7^2/3^3)^3=(3^5)^2/(7^2)^2*(7^~ 2/3^3)^3)~p0 2 ~sb/^! } %( c#T"!c"H" c%X"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})$# b'4" *^: ;bP8&c0!*L/Vsungen,Z| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})$# b'4" *^: ;bP8&c0!*zu 1,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~A((3/4)^2=3/4*3/4)~p0 3 ~sb/^! } %( c#T"!c"\" c"H"_c/__c/__} ^ _~A(~ (3/4)^2=9/16)~p0 4 ~sb/_! } !& c#T"!c%X"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})"# b'4" *^: ;bP8&c0!*oder,Z| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 4 ~A((3/4)^2=3^2/4^2)~p0 5 ~sb/^! } %& c#T"!c%X"_c/__c/__} ^ _~A((3/~ 4)^2=9/4^2)~p0 6 ~sb/_! } !( c#T"!c"\" c%X"_c/__c/__} ^ _~A(~ (3/4)^2=9/16)~p0 7 ~sb/_! } !( c#T"!c"\"!c%X"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 7 ~A((3/4)^2=(3/4)^2)~p0 8 ~sb/_! } !* c#T"!c"\" c%X"!c"L"_c/__c/__} ^ _~ ~A((3/4)^2=(3/4)^2)~p0 9 ~sb/_! } %& c#T"!c"\"_c/__c/__} ^ _~A((3/~ 4)^2=(3/4)^2)~p0 10 ~sb/_! } !( c#T"!c%X"!c"L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})$# b'4" *^: ;bP8&c0!*Zu 2,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~A((4/5^2)^3=4/25*(4/25*4/25))~p0 3 ~sb/^! } "& c#T"!c"H"_c/__c/__} ^ _~A((4/~ 5^2)^3=64/15625)~p0 4 ~sb/_! } !& c#T"!c"H"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})"# b'4" *^: ;bP8&c0!*oder,Z| |}& b!( b"0 b#8 b$@ b%H 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