Site hosted by Angelfire.com: Build your free website today!

#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]);

f := .1*exp(-.3*x)*(x^2-x)*sin(2*x)

[Maple Plot]

#2

>    restart;
plot([max(0.1*x, x*sin(x)),1.2], x=0..12);

[Maple Plot]

>    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);

1.260273805

2.676718762

6.469744336

9.295319422

12.00000000

#3

>    restart;
isprime(32767);
ifactor(32767);

false

``(7)*``(31)*``(151)

>    isprime(65535);
ifactor(65535);

false

``(3)*``(5)*``(17)*``(257)

>    isprime(131071);
ifactor(131071);

true

``(131071)

>    isprime(262143);
ifactor(262143);

false

``(3)^3*``(7)*``(19)*``(73)

>    isprime(524287);
ifactor(524287);

true

``(524287)

>    isprime(1048575);
ifactor(1048575);

false

``(3)*``(5)^2*``(11)*``(31)*``(41)

>    isprime(2097151);
ifactor(2097151);

false

``(7)^2*``(127)*``(337)

>    isprime(4194303);
ifactor(4194303);

false

``(3)*``(23)*``(89)*``(683)

>    isprime(8388607);
ifactor(8388607);

false

``(47)*``(178481)

#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]);

p[1] = x^2

>    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 := 2

p[2] = x^4+x^2

>    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 := 3

p[3] = x^6+3*x^4+2*x^2

>    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]);

p[4] = x^8+6*x^6+11*x^4+6*x^2

>    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]);

p[5] = x^10+10*x^8+35*x^6+50*x^4+24*x^2

#5

>    restart;
Digits:=500:
evalf(Pi);

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819...
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819...
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819...
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819...
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819...

#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]]);

>   

[Maple Plot]