Question: How do you graph banding lines of a function?

Hi,

I am trying to complete this assignment but I am having trouble on this question. It is asking me to use a graphical approach to estimate a 𝛿 > 0 such that for all x...

0 < | x - c | < 𝛿 implies that | f(x) - L | < ε

It says I can do this by plotting my f(x), y₁, and y₂ over the interval [c - 𝛿, c + 𝛿] with a y-range of [L - ε, L + ε]. y₁, and y₂ are banding lines defined by ( L - ε ) and ( L + ε ), respectively. The value of ε is shown below. I dont know where to start but this is what I have so far...

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

The limit ( L ) of this function as x approaches 0 ( c = 0 ) is...

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

The limit is 3 ( L = 3 ).

 ε = r = Student Id / 5000000   = 0621748 / 5000000   = 155337 / 1250000

 ε := 155337 / 1250000;

y₁ := ( L - ε );

y₂ := ( L + ε );

Originally, it had asked me to graph the function with the banding lines (y₁, y₂) together within the interval [-0.2, 0.2], which I have done. I just do not know how to find a value for 𝛿 in this case. Please help.

Thanks.