~v350 300 yz#gVWi]bWbTbWk\hDamjD]] yzwx$NeS^TcUdVmOPVWYTRMUPT_UhVQWfXc ~w58 633 926 547 0 0 0 0 ~f? 14 12 10 ? 3 1 1 0 ? ? ? "Times New Roman" ? ? ? 0 ? 1 1 "Times" 12 ? ? 5 0 c n 16 1 0 0 k 468 i"?n page ?p?a" ? 1 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| |K!Y.N| |9}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~V?m0 (LOPPU)~p0 1 ~V?v0 (loppukohta)~p0 1 ~V?v0 (alkukohta)~p0 1 ~V?v0 (alku)~p0 1 ~V?m0 (ALKU)~p0 1 ~V?v0 (yy)~p0 1 ~V?m0 (P)~p0 1 ~V?f0 (g)~p0 1 ~V?f0 (f)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP7&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f276 (arccsc)~p0 2 ~V?f278 (arccot)~p0 2 ~V?f256 (sin)~p0 2 ~V?f257 (cos)~p0 2 ~V?f258 (tan)~p0 2 ~V?f261 (sec)~p0 2 ~V?f260 (csc)~p0 2 ~V?f262 (cot)~p0 2 ~V?f272 (arcsin)~p0 2 ~V?f273 (arccos)~p0 2 ~V?f274 (arctan)~p0 2 ~V?f277 (arcsec)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP7&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f309 (arcsech)~p0 2 ~V?f304 (arcsinh)~p0 2 ~V?f294 (coth)~p0 2 ~V?f310 (arccoth)~p0 2 ~V?f306 (arctanh)~p0 2 ~V?f293 (sech)~p0 2 ~V?f288 (sinh)~p0 2 ~V?f289 (cosh)~p0 2 ~V?f290 (tanh)~p0 2 ~V?f305 (arccosh)~p0 2 ~V?f308 (arccsch)~p0 2 ~V?f292 (csch)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP7&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f32 (log)~p0 2 ~V?f307 (ln)~p0 2 ~V?f291 (exp)~p0 2 ~V?c2 (e)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP7&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP7&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?x^(-?y)):(1/?x^?y)~p0 3 ~Hs(exp(?z)):(e^?z)~p0 3 ~Hs(e^(ln(?x))):(?x)~p0 3 ~Hs(10^(log(?x))):(?x)~p0 3 ~Hs(?y^(log_?y(?x))):(?x)~p0 3 ~Hs(ln(e^?x)):(?x)~p0 3 ~Hs(log(10^?x)):(?x)~p0 3 ~Hs(log_?y(?y^?x)):(?x)~p0 3 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 3 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 3 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 3 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 3 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 3 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 3 ~He(ln(?u^?v)):(?v*ln(?u))~p0 3 ~He(log(?u^?v)):(?v*log(?u))~p0 3 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 3 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 3 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 3 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 3 ~He(?z^(?x+?y)):(?z^?x*?z^?y)~p0 3 ~He(?z^(?x-?y)):(?z^?x*?z^(-?y))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP7&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP7&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sin(-?x)):(-sin(?x))~p0 4 ~Hs(cos(-?x)):(cos(?x))~p0 4 ~Hs(tan(-?x)):(-tan(?x))~p0 4 ~Hs(sin('p)):(0)~p0 4 ~Hs(sin(?n*'p)):(0)~p0 4 ~Hs(cos(1/2*'p)):(0)~p0 4 ~Hs(cos(?n/2*'p)):(0)~p0 4 ~Hs(-(cos(?x))^2-(sin(?x))^2):(-1)~p0 4 ~Hs(cos('p/2)):(0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP7&c0!*Transform to basic| | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 4 ~Ht(csc(?x)):(1/(sin(?x)))~p0 4 ~Ht(sin(?x)):(1/(csc(?x)))~p0 4 ~Ht(sec(?x)):(1/(cos(?x)))~p0 4 ~Ht(cos(?x)):(1/(sec(?x)))~p0 4 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP7&c0!*Trig Addition| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0 4 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0 4 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0 4 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0 4 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*~ sin((?n-1)*?x))~p0 4 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*~ sin((?n-1)*?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b$L" *|: ;bP7&c0!*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 4 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 4 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 4 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 4 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 4 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 4 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" *|: ;bP7&c0!*substituting | |z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H| |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 4 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP7&c0!*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 4 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 4 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 4 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 4 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b!T" *|: ;bP7&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP7&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sinh(-?x)):(-sinh(?x))~p0 4 ~Hs(cosh(-?x)):(cosh(?x))~p0 4 ~Hs(tanh(-?x)):(-tanh(?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP7&c0!*Transform into | |other types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sinh(?x))^2):((cosh(?x))^2-1)~p0 4 ~Ht((cosh(?x))^2):(1+(sinh(?x))^2)~p0 4 ~Ht((tanh(?x))^2):(1-(sech(?x))^2)~p0 4 ~Ht(sinh(?x)):((e^?x-e^(-?x))/2)~p0 4 ~Ht(cosh(?x)):((e^?x+e^(-?x))/2)~p0 4 ~Ht(tanh(?x)):((e^?x-e^(-?x))/(e^?x+e^(-?x)))~p0 4 ~Ht(tanh(?x)):((sinh(?x))/(cosh(?x)))~p0 4 ~Hs((cosh(?x))^2-(sinh(?x))^2):(1)~p0 4 ~Hs(-(cosh(?x))^2+(sinh(?x))^2):(-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP7&c0!*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0 4 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0 4 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0 4 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP7&c0!*Constants| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?c6 (C)~p0 2 ~V?c5 ('o)~p0 2 ~V?c1 ('p)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?c4 (i)~p0 2 ~V?c3 ('N)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP7&c0!*Variables| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?v0 (n)~p0 2 ~V?v0 (h)~p0 2 ~V?v0 (v)~p0 2 ~V?v0 (u)~p0 2 ~V?v0 (w)~p0 2 ~V?v0 ('f)~p0 2 ~V?v0 ('r)~p0 2 ~V?v0 ('q)~p0 2 ~V?v0 (r)~p0 2 ~V?v0 (t)~p0 2 ~V?v0 (z)~p0 2 ~V?v0 (y)~p0 2 ~V?v0 (x)~p0 2 ~V?v0 (k)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP7&c0!*Functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f162 (max)~p0 2 ~V?f161 (min)~p0 2 ~V?f132 (FromSpherical)~p0 2 ~V?f130 (FromCylindrical)~p0 2 ~V?f128 (FromPolar)~p0 2 ~V?f144 (RowsOf)~p0 2 ~V?f146 (ColsOf)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *|: ;bP7&c0!*Names to the back| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f0 (dlim)~p0 3 ~V?f0 (SAEQN)~p0 3 ~V?f0 (SA)~p0 3 ~V?f0 (D)~p0 3 ~V?f0 (N)~p0 3 ~V?v0 (xSV)~p0 3 ~V?d16 (d)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})b!-# b'4" *|: ;bP8&c0!*Yhdistetyn funktion| | havainnollistus,N Sininen suuri t/Dpl/D on piste ,Ha,L g,Hf,H| |a,I,I,I,N K/Dynnist/D ja sammuta animaatio klikkaamalla kuvaa| |,N Jos haluat muuttaa funktioita,L k/Dyt/D yl/Dreunan INPUT MATH| | ,M valikkoa,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})*# b'4" *|: ;bP8&c0!*Funktio f ,Horanssi| | viiva,I,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(f(?x)=0.10000000000000001*?x^2)~p0 0 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})*# b'4" *|: ;bP8&c0!*Funktio g ,Hpunainen| | viiva,I,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(g(?x)=2*?x+1)~p0 0 ~d~A(alkukohta=1)~p0 0 ~d~A(loppukohta=4)~p0 0 ~d~A(y_1=f(x))~p0 0 ~A(y_1=0.10000000000000001*x^2)~p0 1 ~d~sb/_!!! } b00&!! c#T"_c/__c/__!"} ^ _~G1 1 366 470 2 2 5 4 30 (~ -3.4000000000000004...6.6000000000000005):(-0.70000000000000007...~ 4.6000000000000005):(a=alkukohta...loppukohta):(~ 1/30*loppukohta-1/30*alkukohta):(30)~Q ]|Expr|[#b @`bb#_b#_b#_})%# b#@" *|: ;bP8&c0!*Graph Building | |Blocks}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~A(a=1.8)~p0 1 ~d~R11184810 ? (x,y_1):(y_1=bottom...top):(x=left...~ right):(1)~p0 1 ~R11184810 ? (x,y_1):(x=left...right):(y_1=bottom...~ top):(1)~p0 1 ~X2 5592405 (max(left,min(0,right)),y_1):(y_1=~ bottom...top):(y_1)~p0 1 ~X1 5592405 (x,max(bottom,min(0,top))):(x=left...~ right):(x)~p0 1 ~V?c64 (left)~p0 1 ~V?c65 (right)~p0 1 ~V?c66 (bottom)~p0 1 ~V?c67 (top)~p0 1 ~L2 16744448 ? (x,y_1):(x=left...right)~p0 0 ~L2 16711680 ? (x,y_2):(x=left...right)~p0 0 ~S4 ? 255 ? ? ((P_1)_(k_9,1),(P_1)_(k_9,2)):(k_~ 9=1...RowsOf(P_1)):(5)~p0 0 ~S4 ? 255 ? ? ((P_2)_(k_10,1),(P_2)_(k_10,2)):(~ k_10=1...RowsOf(P_2)):(5)~p0 0 ~S4 ? 255 ? ? ((P_3)_(k_11,1),(P_3)_(k_11,2)):(~ k_11=1...RowsOf(P_3)):(5)~p0 0 ~S21 ? 255 ? ? ((P_4)_(k_12,1),(P_4)_(k_12,2)):(~ k_12=1...RowsOf(P_4)):(10)~p0 0 ~L1 0 ? (a,y):(y=0...f(a))~p0 0 ~L3 0 ? (f(a),y):(y=0...g(f(a)))~p0 0 ~S4 ? 255 ? ? ((P_5)_(k_13,1),(P_5)_(k_13,2)):(~ k_13=1...RowsOf(P_5)):(5)~p0 0 ~L8 8404992 ? (x,yy):(x=left...right)~p0 0 ~S21 ? 255 ? ? (ALKU_(k_14,1),ALKU_(k_14,2)):(~ k_14=1...RowsOf(ALKU)):(10)~p0 0 ~L1 0 ? (x,y_5):(x=0...a)~p0 0 ~L1 0 ? (x,f(a)-x):(x=0...f(a))~p0 0 ~L1 0 ? (f(a),y):(y=0...g(f(a)))~p0 0 ~L1 0 ? (x,g(f(a))):(x=f(a)...a)~p0 0 ~L3 0 ? (x,g(f(a))):(x=0...f(a))~p0 0 ~Y22 1 ? ? 8404992 (a,-2):(a,0)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP8&c0!*a| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Y22 1 ? ? 8404992 (f(a),-2):(f(a),0)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" *|: ;bP8&c0!*f,Ha,I| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Y22 1 ? ? 8404992 (-2,f(a)):(0,f(a))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" *|: ;bP8&c0!*f,Ha,I| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Y22 1 ? ? 8404992 (-2,g(f(a))):(0,g(f(a)))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *|: ;bP8&c0!*g,Hf,Ha,I,I| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~L3 0 ? (a,y):(y=f(a)...g(f(a)))~p0 0 ~S21 ? 255 ? ? (LOPPU_(k_15,1),LOPPU_(k_15,2)):(~ k_15=1...RowsOf(LOPPU)):(10)~p0 0 ~t~p0 2 ~A(y_2=g(x))~p0 0 ~A(y_2=2*x+1)~p1 1 ~d~sb/_!!! } b00&!! c#T"_c/__c/__!"} ^ _~A(P_~ 1=(a,0))~p0 2 ~d~A(P_2=(0,f(a)))~p0 2 ~d~A(P_3=(f(a),0))~p0 2 ~d~A(P_4=(a,g(f(a))))~p0 2 ~d~A(P_5=(0,g(f(a))))~p0 2 ~d~A(y_3=f(a))~p0 2 ~d~A(y_4=g(f(a)))~p0 2 ~d~A(x_1=a)~p0 2 ~d~A(ALKU=(alkukohta,g(f(alkukohta))))~p0 2 ~d~A(LOPPU=(loppukohta,g(f(loppukohta))))~p0 2 ~d~A(y_5=f(a))~p0 2 ~d~A(y_6=1)~p0 2 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})(# b'4" *|: ;bP8&c0!*Yhdistetty funktio| | ,Hpisteviiva,I,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(yy=g(f(x)))~p0 0 ~A(yy=2*f(x)+1)~p0 1 ~sb/_!!! } b00(!! c#T"!c#L"_c/__c/__!"} ^ _~A(~ yy=0.20000000000000001*x^2+1)~p0 2 ~sb/_!!! } b00*!! c#T"!c%X" c#L"_c/__c/__!"} ^ _~ ~A(yy=0.20000000000000001*x^2+1)~p0 3 ~d~sb/_!! } "&! c#T"!c%X"_c/__c/__} ^ _~c2 175 -1 174 -1 169 -1 ~c2 178 -1 177 -1 171 -1 ~c2 193 -1 192 -1 171 -1 ~c2 194 -1 193 -1 169 -1 ~c1 195 -1 194 -1 ~e