The aim here is to find the limit of [ sin(x+h)-sin(x) ]/h as h tends to zero. We will start a plot of the process with h=0.001.
- Make sure your calculator is on Radian mode.
- Set your window: Xmin=0, Xmax = 2p, Xscl=0.5p,
Ymin=-1.25, Ymax= 1.25 & Yscl=1
- Press [Y=]. At Y1=, enter (sin(x+0.001)-sin(x))/0.001.
Note that h is allowed to be 0.001. You could choose to have a smaller h.
- Plot the graph. Observe your graph. What is the limit of our process [ sin(x+h)-sin(x) ]/h as h tends to zero?
- Enter your guess into Y2 and plot. How close is the process to your guess? Look at the table by pressing [2 nd] [graph]. Compare the values in Y1 and Y2.
We can now investigate the limit of [ cos(x+h)-cos(x) ]/h as h tends to zero by simply returning to [Y=] and press.
Repeat this exploration for tan(x), ex and ln (x).
- Go to Y1 and place your cursor in on "s" of sin and press [Del]. This will delete sin.
- Press [2 nd] [Del] to insert.
- Press [cos] and move on to the next "s" of sin and [Del]. Insert cos.
- Repeat (iv) and (v) in Exploration 1.