1.mws

Evaluate the following expressions:

> 123!;

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

> 10!;

3628800

> evalf(123!);

.1214630437e206

> evalf(10!);

3628800.

> evalf(Pi,20);

3.1415926535897932385

> simplify(a/b+c/d);

(a*d+c*b)/(b*d)

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

a^2+2*a*b+2*a*c+b^2+2*c*b+c^2

> factor(x^12-1);

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

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

(x^2+1)*(1-x+x^2)*(x^2-x*sqrt(3)+1)*(x^2+x*sqrt(3)+...

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

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

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

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

> ifactor(18);

``(2)*``(3)^2

> ifactor(2^100+1);

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

> expand(2^100+1);

1267650600228229401496703205377

> diff(x^4,x);

4*x^3

> diff(x^4,x$2);

12*x^2

> int(x^4,x);

1/5*x^5

> int(x^4*cos(3*x)*exp(2*x),x);

(2/13*x^4+20/169*x^3-552/2197*x^2+2856/28561*x+2928...
(2/13*x^4+20/169*x^3-552/2197*x^2+2856/28561*x+2928...

> 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*...

> expand(cos(3*a));

4*cos(a)^3-3*cos(a)

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

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

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

{x = 1/2, y = 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(k^2,k=1..n);

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

> expand(sum(k,k=1..n));

1/2*n^2+1/2*n

> implicitdiff(x^2*y+y^3*x-y,y,x);

-y*(2*x+y^2)/(x^2+3*y^2*x-1)

> implicitdiff(x^2*y+y^3*x-y,x,y);

-(x^2+3*y^2*x-1)/(y*(2*x+y^2))

> 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*163^(1/2)),30);

262537412640768744.000000000024

>