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HOJA DE PRÁCTICA MAPLE
Complejos: s := 4 + 2*I; s d 4 C 2 I m := polar(2,Pi/4); m d polar 2, p 4 polar(s);evalc(m); polar 2 5 , arctan
2 C I 2
evalf(m); polar 2., 0. conjugate(2+3I); 2 K 3 I Re(2+3I);Im(2+3I); 2 3 Re(polar(2,Pi/3));Im(polar(2,Pi/3)); 1 3 abs(2+3I);argument(2+3*I); 13 arctan
abs(polar(2,Pi/4));argument(polar(2,Pi/4)); 2 p 4 assume(a,real);assume(b,real);Re(a+bI); Im(a+bI); a~ b~ z1:=1+3I;z2:=polar(2,Pi/4);z3:=3-5I; z1 d 1 C 3 I z2 d polar 2, p 4 z3 d 3 K 5 I evalc(z1-z2);polar(z1-z2); 1 K 2 C I 3 K 2
polar 1 K 2 2 C 3 K 2 2 , arctan
3 K 2
1 K 2
C p evalc(z1z2);polar(z1z2); K 2 2 C 4 I 2 polar 2 10 , Karctan 2 C p evalc(z2^3);polar(z2^3); K 4 2 C 4 I 2 polar 8, 3 p 4 z:=I;polar(z); z d I polar 1, p 2 z0:=polar(root4, Pi/8); z1:= polar(root4, Pi/8+2Pi/4); z2:=polar(root4, Pi/8+22Pi/4); z3:=polar(root4, Pi/8+32Pi/4); z0 d polar 1, p 8 z1 d polar 1, 5 p 8 z2 d polar 1, 9 p 8 z3 d polar 1, 13 p 8 n:=4: r:=1: arg:=Pi/2: for k from 0 to n-1 do arrel[k]:=polar(rootn,arg/n+2kPi/n) end do; arrel 0 d polar 1, p 8 arrel 1 d polar 1, 5 p 8 arrel 2 d polar 1, 9 p 8 arrel 3 d polar 1, 13 p 8 for k from 0 to n-1 do arrel[k]:=rootnexp((arg/n+2kPi/n)* I) end do;
evalf(sin(Pi/4));
f(x); x 2 x! 1 2 x K 1 otherwise plot(2sin(x)+x,x=-Pi..2Pi); x Kp (^) Kp 2 (^0) p 2 p 3 p 2 2 p K 3 K 2 K 1 1 2 3 4 5 6 plot(2sin(x)+x,x=-Pi..2Pi,y=-2..4,color=blue); x Kp (^) Kp 2 (^0) p 2 p 3 p 2 2 p y K 2 K 1 1 2 3 4 F:=x->-x^2-2*x+3; F d x ↦ Kx 2 K 2 x C 3 plot(F(x),x=-1..2);
x K 1 0 1 2 K 5 K 4 K 3 K 2 K 1 1 2 3 4 plot(x^3-17.5x^2+66.5x-50,x=-50..50); x K 40 K 20 0 20 40 K 150000 K 100000 K 50000 50000 plot(x^3-17.5x^2+66.5x-50,x=-2..14); x K 2 0 2 4 6 8 10 12 14 K 200 K 100 100 plot(exp(x)-sin(x),x=-5..5);
x K 5 0 5 10 K 200 K 100 100 200 300 plot(h(x),x=-5..10,discont=true); x K 5 0 5 10 K 200 K 100 100 200 300 plot([2*sin(x)+x,F(x),3],x=-3..6,color=[green,blue,red]); x K 3 K 2 K 1 0 1 2 3 4 5 6 K 40 K 30 K 20 K 10 with(plots): graf1:=plot(sin(x),x=-Pi..Pi,color=blue): graf2:=plot(exp(x),x=-2..1,color=green): display(graf1,graf2);
x Kp (^) K 3 p 4 K p 2 K p 4 (^0) p 4 p 2 3 p 4 p K 1 1 2 limit(x/(sqrt(x^2+1)-1),x=0); undefined limit(x/(sqrt(x^2+1)-1),x=1); 1 2 K 1 limit(x/(sqrt(x^2+1)-1),x=infinity);limit(x/(sqrt(x^2+1)-1),x=- infinity); 1 K 1 limit(sin(1/x),x=0); K1 .. f:=x->1/(x-2); f d x ↦
x K 2 limit(f(x),x=2,left); KN limit(f(x),x=2,right); N limit(f(x),x=2); undefined h:=x->piecewise(x<=-1,x^4-250,x<5,30x+5,10ln(x-5)); h d x ↦ x 4 K 250 x % K 1 30 x C 5 x! 5 10 ln x K 5 otherwise discont(h(x),x); K1, 5 limit(h(x),x=-1,left); limit(h(x),x=-1,right); K 249 K 25 limit(h(x),x=5,left); limit(h(x),x=5,right);
DiagonalMatrix([2,3]); 2 0 0 3 k:= Vector([2,3]);DiagonalMatrix(k); k d
Transpose (M); K 1 3 4 1 7 5 3 9 8 F:= Matrix([[3,2,1],[5,6,9],[7,0,1]]); F d
M+F;
w:= Vectorrow; w d 3 4 5 w+v; 6 11 14 3M; K 3 3 9 9 21 27 12 15 24 3(M+F); 6 9 12 24 39 54 33 15 27 2*(w+v); 12 22 28 M.F;
e:= Vector([1,2,3]); e d
M.e; 10 44 38 M^4; 2680 4743 7134 12294 21919 33012 10157 18125 27307 M^(-1); K
K
K
K
K
MatrixInverse(M); K
K
K
K
K
Determinant(M); K 38 Rank(M); 3 ;
K 1
A:= Matrix([[3,0,0,4],[0,-1,0,2],[1,0,3,0],[4,-3,0,2]]); A d
0 K 1 0 2
4 K 3 0 2
v:= Vector([26,7,14,9]); v d
H:=; H d
0 K 1 0 2 7
4 K 3 0 2 9
GenerateMatrix([3x+4t=26,-y+2t=7,x+3z=14,4x-3y+2*t=9],[x,y, z,t]); 3 0 0 4 0 K 1 0 2 1 0 3 0 4 K 3 0 2
A,v:= GenerateMatrix({3x+4t=26,-y+2t=7,x+3z=14,4x-3y+2*t=9} ,[x,y,z,t]); A, v d
0 K 1 0 2
4 K 3 0 2
GenerateMatrix({3x+4t=26,-y+2t=7,x+3z=14,4x-3y+2*t=9},[x,y, z,t], augmented=true ); 1 0 3 0 14 3 0 0 4 26 0 K 1 0 2 7 4 K 3 0 2 9
>> s:= GenerateEquations(H,[x,y,z,t]); s d 3 x C 4 t = 26, Ky C 2 t = 7, x C 3 z = 14, 4 x K 3 y C 2 t = 9 eq1:=s[1];eq2:=s[2];eq3:=s[3];eq4:=s[4]; eq1 d 3 x C 4 t = 26 eq2 d Ky C 2 t = 7 eq3 d x C 3 z = 14 eq4 d 4 x K 3 y C 2 t = 9 solve({3x+4t=26,-y+2t=7,x+3z=14,4x-3y+2*t=9}); t = 5, x = 2, y = 3, z = 4 A:= Matrix([[3,0,0,4],[0,-1,0,2],[1,0,3,0],[4,-3,0,2]]); v:= Vector([26,7,14,9]); A d
0 K 1 0 2
4 K 3 0 2
v d
LinearSolve(A,v); 2 3 4 5 H:=; H d
0 K 1 0 2 7
4 K 3 0 2 9
LinearSolve(H); 2 3 4 5 A^(-1).v;
Derivades: f:=x->x^3+2*x^2-1; f d x ↦ x 3 C 2 x 2 K 1 D(f); x ↦ 3 x 2 C 4 x diff(f(x),x); 3 x 2 C 4 x D(f)(3.02);
plot(D(f)(x),x=-3..1); x K 3 K 2 K 1 0 1 5 10 15 solve(D(f)(x)>0,x); KN, K
, 0, N
df:= diff(f(x),x); df d 3 x 2 C 4 x eval(df,x=1); subs(x=1,df); 7 7 df:=unapply(df,x); df(1); df d x ↦ 3 x 2 C 4 x 7 solve(df(x)>0,x); KN, K
, 0, N
f := x -> x^4; f d x ↦ x 4 limit((f(1+h)-f(1))/h,h=0); limit((f(x)-f(1))/(x-1),x=1); 4 4
g:=x->abs(x-5); g d x ↦ x K 5 limit((g(5+h)-g(5))/h,h=0); undefined limit((g(5+h)-g(5))/h,h=0,left); limit((g(5+h)-g(5))/h,h=0,right) ; K 1 1 f:=x->x^3+2*x^2-1; f d x ↦ x 3 C 2 x 2 K 1 D(D(f)); x ↦ 6 x C 4 diff((f(x),x,x)); 6 x C 4
(D@@3)(f);
diff((f(x),x$3)); 6 plot((D@@2)(f)(x),x=-3..1); x K 3 K 2 K 1 0 1 K 10 K 5 5 10 solve((D@@2)(f)(x)>0,x); K
, N
df1:=D(f); df1 d x ↦ 3 x 2 C 4 x df2:=(D@@2)(f); df2 d x ↦ 6 x C 4 df1(3.02);
plot(df2(x),x=-3..1);
x K 6 K 4 K 2 0 2 4 6 K 6 K 4 K 2 2 4 6 showtangent(f(x),x=1.5,x=1..2); x 1 1.2 1.4 1.6 1.8 2 0
1
2 abs(f(1.5)-t(1.5)); abs(f(1.501)-t(1.501)); abs(f(1.51)-t(1.51)); abs(f(1.6)-t(1.6)); abs(f(2.5)-t(2.5));
6.78 10K^7
taylor(sin(x),x=0,6); x K
x 3 C
x 5 C O x 7 3.^(9+1)/(9+1)!;
3.^(10+1)/(10+1)!;
evalf(abs(3-Pi)^3/3!);
pAlt1:=unapply(convert(taylor(sin(x),x=Pi,3),polynom),x); pAlt1 d x ↦ Kx C p evalf(pAlt1(3));
pAlt2:=unapply(convert(taylor(sin(x+Pi),x=0,3),polynom),x); pAlt2 d x ↦ Kx evalf(pAlt2(3-Pi));
Integracio; int((sin(x))^2,x); K sin x cos x 2
C
x 2 Int((sin(x))^2,x); sin x 2 dx f:=x->x^2; f d x ↦ x 2 int(f(x),x); x 3 3 int((sin(t))^2,t=0..Pi); p 2 evalf(int((sin(t))^2,t=0..Pi));
f:=x->1+2*sin(x); f d x ↦ 1 C 2 sin x plot(f(x),x=-Pi..Pi);
