hw1.mws

> 123!;

121463043670253296757662432418812958554542170884833...
121463043670253296757662432418812958554542170884833...
121463043670253296757662432418812958554542170884833...

> 100!;

933262154439441526816992388562667004907159682643816...
933262154439441526816992388562667004907159682643816...

> 10!;

3628800

> evalf(123!);

.1214630437e206

> simplify(d/c+ab/d);

(d^2+ab*c)/(c*d)

> expand((a+b+2*c)^3);

a^3+3*a^2*b+6*a^2*c+3*a*b^2+12*a*b*c+12*a*c^2+b^3+6...

> factor(x^10-1);

(x-1)*(x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)

> factor(x^12-1,2^(1/2));

(x^2-x+1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1)*(x+1)*(x-1)...

>

> factor(x^12-1,I);

(x^2-x+1)*(x^2+x+1)*(x^2+I*x-1)*(x^2-I*x-1)*(x+I)*(...

> factor(x^12-1,{3^(1/2),I});

1/256*(2*x-1-I*sqrt(3))*(2*x-1+I*sqrt(3))*(x+I)*(x-...
1/256*(2*x-1-I*sqrt(3))*(2*x-1+I*sqrt(3))*(x+I)*(x-...

> ifactor(2^100+1);

``(17)*``(401)*``(3173389601)*``(61681)*``(2787601)...

> ifactor(3^2+1);

``(2)*``(5)

> diff(x^6,x);

6*x^5

>

>

>

> diff(x^6,x$4);

360*x^2

> int(x^6,x$1);

1/7*x^7

> int(x^2*cos(2*x)* exp(2*x),x);

1/8*(2*x^2-1/2)*exp(2*x)*cos(2*x)-1/8*(-2*x^2+2*x-1...

> evalf(int(cos(x^2),x=0..1));

.9045242380

> series(cos(x),x=0,20);

series(1-1/2*x^2+1/24*x^4-1/720*x^6+1/40320*x^8-1/3...
series(1-1/2*x^2+1/24*x^4-1/720*x^6+1/40320*x^8-1/3...

> combine(cos(a)*cos(b));

1/2*cos(a-b)+1/2*cos(a+b)

> expand(cos(a+b));

cos(a)*cos(b)-sin(a)*sin(b)

> combine(cos(a)*cos(b)*cos(c));

1/4*cos(-c+a-b)+1/4*cos(c+a-b)+1/4*cos(-c+a+b)+1/4*...

> solve(x^2-3*x-7);

3/2+1/2*sqrt(37), 3/2-1/2*sqrt(37)

> solve((x^2-3)*(x-7));

7, sqrt(3), -sqrt(3)

> solve({2*x+3=4,3*x-y=1});

{y = 1/2, x = 1/2}

> solve({x+y+z=1,2*x+y-3=0},{x,y});

{x = 2+z, y = -1-2*z}

> simplify(1/(1+1/(1+x)));

(1+x)/(2+x)

> sum(d^3,d=1..10);

3025

> sum(k^2,k=1..n);

1/3*(n+1)^3-1/2*(n+1)^2+1/6*n+1/6

> implicitdiff(x^2*y,y,x);

-2*y/x

> series(x/cos(x^2+x),x=0,10);

series(1*x+1/2*x^3+1*x^4+17/24*x^5+5/6*x^6+961/720*...

> evalf(exp(Pi*123^(1/2)),30);

1354146840466852.22923438145134

>