Ex17.mw

> Exercice 15

> restart;

a)

> Equation1:=1>abs(x-1);sol1:=solve(Equation1,x);

Equation1 := abs(x-1) < 1

sol1 := RealRange(Open(0), Open(2))

> assume(x>0,x<2);

> expression:=abs((x**3-3*x+6)/(x**2-16))<6; is(expression);

expression := -(x^3-3*x+6)/(x^2-16) < 6

true

b)

> restart;

> Equation1:=1>abs(x);sol1:=solve(Equation1,x);

Equation1 := abs(x) < 1

sol1 := RealRange(Open(-1), Open(1))

> assume(x>-1,x<1);

> expression:=abs((x+sin(x))/(x**7+x-3))<=2; is(expression);

expression := abs((x+sin(x))/(x^7+x-3)) <= 2

true

c)

> restart;

> Equation1:=1/2>abs(x+1);sol1:=solve(Equation1,x);

Equation1 := abs(x+1) < 1/2

sol1 := RealRange(Open((-3)/2), Open((-1)/2))

> assume(x>-3/2,x<-1/2);

> expression:=abs(((x**3+1)*sin(1/x)+(x+1)*(cos(1+exp(x)))**3)/abs(4*x+sin(Pi*x/2)))<23*abs(x+1)/4; is(expression);

expression := abs((x^3+1)*sin(1/x)+(x+1)*cos(1+exp(x))^3)/(-4*x-sin(1/2*Pi*x)) < 23/4*abs(x+1)

FAIL

>