~v200 200 ~w74 4 490 760 460 1449 0 0 ~f? 14 12 10 ? 3 0 1 0 ? ? ? "Times New Roman" ? ? ? 1 ? 0 1 "Times" 12 ? ? 5 0 c n 106 1 0 0 k 468 f"?n page ?p?a" -2 1 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 0 0 -1 -1 -1 -1 -1 1 1 ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})b!"# b'4" *^: ;bP8&c0!*Para fazer o | |que se pede,L altere os pontos de coordenadas ,H1,L4,I,L,Ha,L| | aa,I,L,Hx,L2,I,L ,Hb,Lbb, ,I,N,N,N,Hu,Luu,I,L usados para desenhar| | o peixinho e observe o resultado,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 0 ~V?v0 (uu)~p0 1 ~V?v0 (u)~p0 1 ~V?v0 (oo)~p0 1 ~V?v0 (o)~p0 1 ~V?v0 (jj)~p0 1 ~V?v0 (j)~p0 1 ~V?v0 (hh)~p0 1 ~V?v0 (h)~p0 1 ~V?v0 (gg)~p0 1 ~V?v0 (g)~p0 1 ~V?v0 (ff)~p0 1 ~V?v0 (f)~p0 1 ~V?v0 (mm)~p0 1 ~V?v0 (m)~p0 1 ~V?v0 (cc)~p0 1 ~V?v0 (bb)~p0 1 ~V?v0 (aa)~p0 1 ~V?v0 (w)~p0 1 ~V?v0 (t)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *^: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?c1 ('p)~p0 2 ~V?f256 (sin)~p0 2 ~V?f257 (cos)~p0 2 ~V?f258 (tan)~p0 2 ~V?f261 (sec)~p0 2 ~V?f260 (csc)~p0 2 ~V?f262 (cot)~p0 2 ~V?f272 (arcsin)~p0 2 ~V?f273 (arccos)~p0 2 ~V?f274 (arctan)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *^: ;bP8&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f293 (sech)~p0 2 ~V?f288 (sinh)~p0 2 ~V?f289 (cosh)~p0 2 ~V?f290 (tanh)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *^: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f32 (log)~p0 2 ~V?f307 (ln)~p0 2 ~V?f291 (exp)~p0 2 ~V?c2 (e)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *^: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?x^(-?y)):(1/?x^?y)~p0 3 ~Hs(exp(?z)):(e^?z)~p0 3 ~Hs(e^(ln(?x))):(?x)~p0 3 ~Hs(10^(log(?x))):(?x)~p0 3 ~Hs(?y^(log_?y(?x))):(?x)~p0 3 ~Hs(ln(e^?x)):(?x)~p0 3 ~Hs(log(10^?x)):(?x)~p0 3 ~Hs(log_?y(?y^?x)):(?x)~p0 3 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 3 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 3 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 3 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 3 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 3 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 3 ~He(ln(?u^?v)):(?v*ln(?u))~p0 3 ~He(log(?u^?v)):(?v*log(?u))~p0 3 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 3 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 3 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 3 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *^: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *^: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sin(-?x)):(-sin(?x))~p0 4 ~Hs(cos(-?x)):(cos(?x))~p0 4 ~Hs(tan(-?x)):(-tan(?x))~p0 4 ~Hs(sin('p)):(0)~p0 4 ~Hs(sin(?n*'p)):(0)~p0 4 ~Hs(cos(1/2*'p)):(0)~p0 4 ~Hs(cos(?n/2*'p)):(0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *^: ;bP8&c0!*Transform to basic| | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 4 ~Ht(csc(?x)):(1/(sin(?x)))~p0 4 ~Ht(sin(?x)):(1/(csc(?x)))~p0 4 ~Ht(sec(?x)):(1/(cos(?x)))~p0 4 ~Ht(cos(?x)):(1/(sec(?x)))~p0 4 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&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" *^: ;bP8&c0!*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 4 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 4 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 4 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 4 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 4 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 4 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" *^: ;bP8&c0!*substituting | |z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H| |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 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$L" *^: ;bP8&c0!*Other rules| |}& b!( b"0 b#8 b$@ 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" *^: ;bP8&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *^: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sinh(-?x)):(-sinh(?x))~p0 4 ~Hs(cosh(-?x)):(cosh(?x))~p0 4 ~Hs(tanh(-?x)):(-tanh(?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *^: ;bP8&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" *^: ;bP8&c0!*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0 4 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0 4 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0 4 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&c0!*Integration Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~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 3 ~Hs(ln(?x+?b*i)):((-i*arctan(?x/?b)+1/2*ln(?x^2+?b^2))+1/2*'p*~ i)~p0 4 ~Hs(ln(?x+i)):((-i*arctan(?x)+1/2*ln(?x^2+1))+1/2*'p*i)~p0 4 ~Hs(ln(?x-?b*i)):((i*arctan(?x/?b)+1/2*ln(?x^2+?b^2))+1/2*'p*~ i)~p0 4 ~Hs(ln(?x-i)):((i*arctan(?x)+1/2*ln(?x^2+1))+1/2*'p*i)~p0 4 ~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 3 ~Ht(Diff(?x)*(Integral(?y*d*?x))):(?y)~p0 4 ~V?c4 (i)~p0 1 ~V?d16 (d)~p0 1 ~V?v0 (k)~p0 1 ~V?c0 (n)~p0 1 ~V?c0 (c)~p0 1 ~V?c0 (b)~p0 1 ~V?c0 (a)~p0 1 ~V?v0 (z)~p0 1 ~V?v0 (y)~p0 1 ~V?v0 (x)~p0 1 ~G1 1 299 299 1 1 3 4 10 (-6...6):(-6...6):(?=0...2*'p):('p/5):(~ 10)~Q ]|Expr|[#b @`bb#_b#_b#_})b S# b#@" *^: ;bP8&c0!*Modifique os | |pontos definidos nas linhas abaixo de acordo com o que se pede| | em cada item e veja o efeito sobre o desenho do peixinho| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 0 ~V?v0 (ImplicitDifference)~p0 1 ~A(ImplicitDifference_0=w-(t+2))~p0 1 ~d~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 -1365 -4096 0 65535 -1365 4096 0 ~gc1 2 ? 0 0 -4096 0 65535 0 4096 0 ~gc1 2 ? 0 1365 -4096 0 65535 1365 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 -1365 0 65535 4096 -1365 0 ~gc1 2 ? 0 -4096 0 0 65535 4096 0 0 ~gc1 2 ? 0 -4096 1365 0 65535 4096 1365 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 ~L2 0 ? (1,4):(t=0...1)~p0 0 ~gc1 2 ? 0 683 2731 0 65535 683 2731 0 ~L2 255 ? (a,aa):(t=0...~ 1)~p0 0 ~gc1 3 ? 0 0 2048 0 32767 341 1707 0 65535 683 1365 0 ~L2 255 ? (~ x,2):(t=1...3)~p0 0 ~gc1 2 ? 0 683 1365 0 65535 2048 1365 0 ~L2 255 ? (b,bb):(t=0...~ 1)~p0 0 ~gc1 3 ? 0 2048 1365 0 32767 2731 1707 0 65535 3413 2048 0 ~L2 255 ? (~ c,cc):(t=0...1)~p0 0 ~gc1 2 ? 0 4096 1365 0 65535 4096 3413 0 ~L2 16711680 ? (m,mm):(~ t=0...1)~p0 0 ~gc1 2 ? 0 4096 3413 0 65535 3413 2731 0 ~L2 16711680 ? (f,ff):(~ t=0...1)~p0 0 ~gc1 3 ? 0 3413 2731 0 32767 2731 3072 0 65535 2048 3413 0 ~L2 16711680 ? (~ g,gg):(t=0...1)~p0 0 ~gc1 2 ? 0 2048 3413 0 65535 683 3413 0 ~L2 16711680 ? (h,hh):(~ t=0...1)~p0 0 ~gc1 3 ? 0 683 3413 0 32767 341 3072 0 65535 0 2731 0 ~L2 255 ? (~ j,jj):(t=0...1)~p0 0 ~gc1 2 ? 0 3413 2048 0 65535 4096 1365 0 ~L2 16711680 ? (o,oo):(~ t=0...1)~p0 0 ~gc1 2 ? 0 0 2731 0 65535 341 2389 0 ~L2 255 ? (u,uu):(t=0...~ 1)~p0 0 ~gc1 2 ? 0 341 2389 0 65535 0 2048 0 ~L2 0 ? (1,4):(t=0...1)~p0 0 ~gc1 2 ? 0 683 2731 0 65535 683 2731 0 ~L2 255 ? (a,aa):(t=0...~ 1)~p0 0 ~gc1 3 ? 0 0 2048 0 32767 341 1707 0 65535 683 1365 0 ~L2 255 ? (~ x,2):(t=1...3)~p0 0 ~gc1 2 ? 0 683 1365 0 65535 2048 1365 0 ~L2 255 ? (b,bb):(t=0...~ 1)~p0 0 ~gc1 3 ? 0 2048 1365 0 32767 2731 1707 0 65535 3413 2048 0 ~L2 255 ? (~ c,cc):(t=0...1)~p0 0 ~gc1 2 ? 0 4096 1365 0 65535 4096 3413 0 ~L2 16711680 ? (m,mm):(~ t=0...1)~p0 0 ~gc1 2 ? 0 4096 3413 0 65535 3413 2731 0 ~L2 16711680 ? (f,ff):(~ t=0...1)~p0 0 ~gc1 3 ? 0 3413 2731 0 32767 2731 3072 0 65535 2048 3413 0 ~L2 16711680 ? (~ g,gg):(t=0...1)~p0 0 ~gc1 2 ? 0 2048 3413 0 65535 683 3413 0 ~L2 16711680 ? (h,hh):(~ t=0...1)~p0 0 ~gc1 3 ? 0 683 3413 0 32767 341 3072 0 65535 0 2731 0 ~L2 255 ? (~ j,jj):(t=0...1)~p0 0 ~gc1 2 ? 0 3413 2048 0 65535 4096 1365 0 ~L2 16711680 ? (o,oo):(~ t=0...1)~p0 0 ~gc1 2 ? 0 0 2731 0 65535 341 2389 0 ~L2 255 ? (u,uu):(t=0...~ 1)~p0 0 ~gc1 2 ? 0 341 2389 0 65535 0 2048 0 ~t~p3 0 ~A(x=t)~p0 1 ~d~A(y=-t+3)~p0 255 ~d~A(j=t+5)~p0 2 ~d~A(jj=-t+3)~p0 255 ~d~A(a=t)~p0 2 ~d~A(aa=-t+3)~p0 255 ~d~A(b=2*t+3)~p0 3 ~d~A(bb=t+2)~p0 255 ~d~A(c=6)~p0 3 ~d~A(cc=3*t+2)~p0 255 ~d~A(m=-t+6)~p0 3 ~d~A(mm=-t+5)~p0 255 ~d~A(f=-2*t+5)~p0 3 ~d~A(ff=t+4)~p0 255 ~d~A(g=-2*t+3)~p0 3 ~d~A(gg=5)~p0 255 ~d~A(h=-t+1)~p0 3 ~d~A(hh=-t+5)~p0 255 ~d~A(o=0.5*t)~p0 3 ~d~A(oo=-0.5*t+4)~p0 255 ~d~A(u=-0.5*t+0.5)~p0 3 ~d~A(uu=-0.5*t+3.5)~p0 255 ~d~e