ex7-8-9.mw

> Exercice 7

> F:=u->int(cos(x)/x,x=u..2*u);

F := proc (u) options operator, arrow; int(cos(x)/x, x = u .. 2*u) end proc

> Limit(F(u),u=0,right)=limit(F(u),u=0,right);

Limit(int(cos(x)/x, x = u .. 2*u), u = 0, right) = ln(2)

>

>

>

> Exercice 8

> F:=x->int(ln(t),t=x..x^2);

F := proc (x) options operator, arrow; int(ln(t), t = x .. x^2) end proc

> Diff('F'(x),x)=D(F)(x);

Diff(F(x), x) = 2*x*ln(x^2)-ln(x)

> 'F(x)'=eval(F(x));

F(x) = -x*ln(x)+x+x^2*ln(x^2)-x^2

> plot(rhs(%),x=0..infinity);

[Plot]

>

>

> Exercice 9

> F:=x->int(sqrt(1-t^8),t=x^2/6..3*x^3);

F := proc (x) options operator, arrow; int(sqrt(1-t^8), t = 1/6*x^2 .. 3*x^3) end proc

> Diff('F'(x),x)=D(F)(x);

Diff(F(x), x) = 9*x^2*(1-6561*x^24)^(1/2)-1/3888*x*(1679616-x^16)^(1/2)

> Limit(F(x),x=0)=limit(F(x),x=0);

> plot(F);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Error, empty plot

>