#1
> | restart; f:=0.1*exp(-0.3*x)*(x^2-x)*sin(2*x); plot([f, diff(f,x), diff(diff(f,x),x)], x=-3..2, -6..6, color=[red, green, magenta]); |
#2
> | restart; plot([max(0.1*x, x*sin(x)),1.2], x=0..12); |
> | fsolve(max(0.1*x, x*sin(x))=1.2, x, x=0..2); fsolve(max(0.1*x, x*sin(x))=1.2, x, x=2..4); fsolve(max(0.1*x, x*sin(x))=1.2, x, x=6..8); fsolve(max(0.1*x, x*sin(x))=1.2, x, x=8..10); fsolve(max(0.1*x, x*sin(x))=1.2, x, x=10..12); |
#3
> | restart; isprime(32767); ifactor(32767); |
> | isprime(65535); ifactor(65535); |
> | isprime(131071); ifactor(131071); |
> | isprime(262143); ifactor(262143); |
> | isprime(524287); ifactor(524287); |
> | isprime(1048575); ifactor(1048575); |
> | isprime(2097151); ifactor(2097151); |
> | isprime(4194303); ifactor(4194303); |
> | isprime(8388607); ifactor(8388607); |
#4
> | restart; m:=1: p[m]:=1: for k from 1 to m do p[m]:=p[m]*(x^2-k+m); od: 'p[1]'=expand(p[m]); |
> | m:=2: p[m]:=1: for k from 1 to m do p[m]:=p[m]*(x^2-k+m); od: 'p[2]'=expand(p[m]); |
> | m:=3: p[m]:=1: for k from 1 to m do p[m]:=p[m]*(x^2-k+m); od: 'p[3]'=expand(p[m]); |
> | m:=4: p[m]:=1: for k from 1 to m do p[m]:=p[m]*(x^2-k+m); od: 'p[4]'=expand(p[m]); |
> | m:=5: p[m]:=1: for k from 1 to m do p[m]:=p[m]*(x^2-k+m); od: 'p[5]'=expand(p[m]); |
#5
> | restart; Digits:=500: evalf(Pi); |
#6
> | restart; plot([[cos(t),sin(t),t=0..2*Pi],[2*cos(t),2*sin(t),t=0..2*Pi],[3*cos(t),3*sin(t),t=0..2*Pi],[4*cos(t),4*sin(t),t=0..2*Pi],[5*cos(t),5*sin(t),t=0..2*Pi]]); |
> |