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Manual Maple 2.3.4.mws

Comandos Úteis e Simples

Seção 2.3: Aplicações de Cálculo

Session 2.3.4: series

> restart;

> series( sin(x), x, 13 );

> series( x^x, x, 5 );

> asympt(1/GAMMA(x), x, 3 );

(1/2*2^(1/2)/Pi^(1/2)/(1/x)^(1/2)-1/24*2^(1/2)/Pi^(1/2)*(1/x)^(1/2)+1/576*2^(1/2)/Pi^(1/2)*(1/x)^(3/2)+O((1/x)^(5/2)))*(1/x)^x*exp(x)

> series( sin(x)^(1/3), x );

x^(1/3)-1/18*x^(7/3)-1/3240*x^(13/3)+O(x^(19/3))

> alias(alpha=RootOf(z^3+z+1, z));

> series(RootOf(z^3+(1+x)*z+1, z), x);

> x = t*tan(t);

> map(series, %, t=Pi/4 );

series(x,t=-(-1/4*Pi)) = series(1/4*Pi+(1/2*Pi+1)*(t-1/4*Pi)+(1/2*Pi+2)*(t-1/4*Pi)^2+(2+2/3*Pi)*(t-1/4*Pi)^3+(8/3+5/6*Pi)*(t-1/4*Pi)^4+(16/15*Pi+10/3)*(t-1/4*Pi)^5+O((t-1/4*Pi)^6),t=-(-1/4*Pi),6)

> solve( %, t );

series(1/4*Pi+2*1/(Pi+2)*(x-1/4*Pi)+(-4*(Pi+4)/(Pi+2)^3)*(x-1/4*Pi)^2+16/3*(14*Pi+Pi^2+36)/(Pi+2)^5*(x-1/4*Pi)^3+(-64/3*(9*Pi^2+136+71*Pi)/(Pi+2)^7)*(x-1/4*Pi)^4+(-128/15*(-5800-734*Pi^2+3*Pi^4-3836*Pi...

> restart;

> f := ( sin(tan(x)) - tan(sin(x)) )/x^7;

f := (sin(tan(x))-tan(sin(x)))/x^7

> series( f, x );

>    for k to 5 do
  Order := Order + 1;
  series( f , x );
end do;

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