The question I choose for assinment
1 is below.
I construct two graphs of y = sin x
and of y = (sin 3x - sin x)/2x.
The picture below indicates the curves
of the the two graphs around the area of x = 0 to x = 1.
We can estimate by this picture that
the value of (sin 3x - sin x)/2x is approach to 1 although we
know there is no value just for the point where x = 0.
By Spread Sheet of Excel, you can review
the values of the functions above.
The values of cells are shown from
x = 1 down to x = 0, with one step 0.05.
As you see, the value of (sin 3x -
sin x)/2x aproaches to 1 and when x = 0 there is no value for
(sin 3x - sin x)/2x.
By another spread sheet, I describe
more detailed values from 0.05 down to 0 with one step 0.0025.
I show you arithmetically that the
value of (sin 3x - sin x)/2x converges to 1 with x being to 0