SITE-C teams: Lesson 14

Apply the Squeeze Theorem in the investigation of lim _{x-> ¥
} ^{sin x}/_{x}.

Turn on the **CASIO CFX-9850G** by pressing

Use the cursor arrows to highlight the GRAPH menu and press **EXE **or just press **5** when at the main menu screen.

In the Y1 slot enter sin X ¸
X and press **EXE** to store it in memory.

In the Y2 slot enter 1 ¸
X and press **EXE** to store it in memory. Use the up cursor arrow to highlight Y2, press **F4** (COLR) **F2** (Orng), and **EXIT**.

In the Y3 slot enter -1 ¸
X and press **EXE** to store it in memory. Use the up cursor arrow to highlight Y2, press **F4** (COLR) **F3** (Grn), and **EXIT**.

Press **SHIFT** **MENU** (SETUP), use the down cursor arrow to scroll down and highlight the Angle line, press **F2** (Rad) **EXIT**.

Press **SHIFT** **F3** (V-Window) **F2** (TRIG).

Press **EXIT** to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press **F6** (DRAW) to see the graph.

See that ^{sin x}/_{x} is squeezed between ^{1}/_{x} and ^{-1}/_{x} as the x values increase.

Press **SHIFT** **F3** (V-Window) to set the parameters as follows:

Xmin = 0 Ymin = -1.6 |
Xmax = 4p Ymax = 1.6 |
Xscale = p /2 Yscale = 0.5 |

Note that the calculator converts 4p
and p
/2 to their decimal equivalent as soon as **EXE** is pressed.

Press** SHIFT F1** (Trace). Use the right cursor arrow to move along the ^{sin x}/_{x} curve to x = 12.067705113. Use the up and down cursor arrows to view y values for each of the ^{1}/_{x} and ^{-1}/_{x} curves. Note that the y values of ^{1}/_{x} approach zero from the positive side while the y values of ^{-1}/_{x} approach zero from the negative side. The ^{sin x}/_{x} y values oscillate between negative and positive but are always between ^{1}/_{x} and ^{-1}/_{x} .

Press **EXIT** **MENU**.

Turn off the **CASIO CFX-9850G** by pressing