The problem itself

(a) Now use fsolve (along with plot ) to find all the intersections of the graphs of and for x between -10 and 10. For each intersection, report both its x -coordinate and its y -coordinate.

(b) How many intersections do you think these curves have (over all values of x, not just from -10 to 10)?

> restart;

> eq1 := x*sin(x):
eq2 := x-cos(x):

> with(plots):
plot1 := plot({eq1,eq2},x=-10..10):
display(plot1);

>

> plot({x*sin(x),x-cos(x)},x=-5..-4);

> x1 := fsolve(eq1=eq2,x=-4.8..-4.6);

> x2 := fsolve(eq1=eq2,x=-4.6..-4);

>

> x3:= fsolve(eq1=eq2,x=1..2);

>

> plot({x*sin(x),x-cos(x)},x=7..8);

> x4 := fsolve(eq1=eq2,x=7..7.7);

> x5 := fsolve(eq1=eq2,x=7.7..8);

> point1:=[x1,y1];point2:=[x2,y2];

> subs({x=point1[1],y=point1[2]},eq1);

>