f:=unapply(sin(x)*cos(x)*exp(x), x);
integrate(f(x), x);
?taylor
f:=unapply(sin(x), x);
t2:=unapply(taylor(f(x), x=Pi/2, 2), x);
t4:=unapply(taylor(f(x), x=Pi/2, 4), x);
t6:=unapply(taylor(f(x), x=Pi/2, 6), x);
?convert
convert(t2(x), polynom);
t2wo:=unapply(convert(t2(x), polynom), x);
t4wo:=unapply(convert(t4(x), polynom), x);
t6wo:=unapply(convert(t6(x), polynom), x);
plot([f(x), t2wo(x), t4wo(x), t6wo(x)], x=-3..8, y=-3..3);
evalf(t6wo(Pi/3));
evalf(sin(Pi/3));
u2:=unapply(convert(taylor(arctan(ln(x)/x), x=Pi/2, 2) , polynom), x );
u4:=unapply(convert(taylor(arctan(ln(x)/x), x=Pi/2, 4) , polynom), x );
?log
u6:=unapply(convert(taylor(arctan(ln(x)/x), x=Pi/2, 6) , polynom), x );
plot([arctan(ln(x)/x), u2(x), u4(x), u6(x)], x=0..3, y=-2..2);
x:=unapply(ln(t)*sin(t), t);
y:=t->ln(t)*cos(t);
plot([x(t), y(t), t=1..24*Pi]);
x:=unapply(sin(t), t);
y:=t->cos(t);
plot([x(t), y(t), t=0..2*Pi]);
x:=sqrt(2^2+2^2)*cos(t);
y:=sqrt(2^2+2^2)*sin(t);
plot([x,y,t=3*Pi/4..7*Pi/4]);
f:=4*exp(-x^2-y^2/4);
L:=Int(sqrt((diff(x,t))^2+(diff(y,t))^2+(diff(f,t))^2), t=3*Pi/4..7*Pi/4);
evalf(L);
F:=4*exp(-X^2-Y^2/4):
with(plots):
A:=spacecurve([x,y,f+0.05], t=3*Pi/4..7*Pi/4, color=red):
B:=plot3d(F,X=-3..3,Y=-3..3, color=blue, axes=framed):
display(A,B);
x_a:=-2;
y_a:=2-4*t;
x_b:=-2+4*t;
y_b:=-2;
L_A:=Int(sqrt((diff(x_a,t))^2+(diff(y_a,t))^2+(diff(f,t))^2), t=0..1);
L_B:=Int(sqrt((diff(x_b,t))^2+(diff(y_b,t))^2+(diff(f,t))^2), t=0..1);
evalf(L_A+L_B);
?display
?spacecurve
f_a:=4*exp(-x_a^2-y_a^2/4);
f_b:=4*exp(-x_b^2-y_b^2/4);
A_A:=spacecurve([x_a,y_a,f_a+0.05], t=0..1, color=red):
A_B:=spacecurve([x_b,y_b,f_b+0.05], t=0..1, color=red):
display(A_A, A_B, B);