Problem 1 

>	f:=x*sin(x)+cos(x);

 

(1.1)

 

>	g:=-x*cos(x)+sin(x);

 

(1.2)

 

>	h:=diff(f,x);

 

(1.3)

 

>	i:=diff(g,x);

 

(1.4)

 

>	with(plots):

 

>	p1:=plot(f,x=-5..5,color=red);

 

(1.5)

 

>	p2:=plot(g,x=-5..5,color=orange);

 

(1.6)

 

>	p3:=plot(h,x=-5..5,color=blue);

 

(1.7)

 

>	p4:=plot(i,x=-5..5,color=brown);

 

(1.8)

 

>	display(p1,p2,p3,p4);

 

>

 

Problem 2 

>	fsolve(f=g,x,-5..0);

 

(2.1)

 

>	fsolve(f=g,x,0..5);

 

(2.2)

 

>

 

Problem 3 

>	z:=sqrt(1-(cos(x))^2)/x;

 

(3.1)

 

>	Limit(z,x=0,right);

 

(3.2)

 

>

evalf(%);

 

(3.3)

 

>	Int(z,x=0..1);

 

(3.4)

 

>

evalf(%);

 

(3.5)

 

>

 

Problem 4 

>	nonsense:=proc(x) local y;

 

>	if x<=10 then y:=x^2;

 

>	else y:=10*x;

 

>

end if;

 

>

return y;

 

>

end proc;

 

(4.1)

 

>	nonsense(2);

 

(4.2)

 

>	nonsense(11);

 

(4.3)

 

>