Mathematical Experiment 1

Evaluate the following expressions:

> 123!;

> evalf(100!);

> evalf(Pi,20);

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

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

> factor(x^12-1);

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

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

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

> ifactor(2^100+1);

> diff(x^4,x);

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

> int(x^4,x);

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

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

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

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

> expand(cos(a+b));

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

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

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

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

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

> sum(k^2,k = 1 .. 20);

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

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

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

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

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