@Carl Love 

In the question it states that  ε = r = Student ID / 5000000, which is          0621748 / 5000000 = 155437 / 1250000. So, with the limit being 3 as x approaches 0, I put:

f(x) := [ x ( 1 - cos(x) ) ] / ( x - sin(x) );

L := (limit(f(x), x=0));

ε := 155437 / 1250000

y1 := (L - ε);

y2 := (L + ε);

plot([ y1, y2, f(x)], x = -0.2 ..0.2);

This is the original function f(x) in the interval [-0.5, 0.5].

I'm very new at this so I apologize for any inconvenience.

@Kitonum 

In the question it says that ε = r = Student ID / 5000000 (my ID is 0621748)

therefore I got 0621748 / 5000000 = 155437 / 1250000.