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 .

Note that.