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 AC/ON.

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 SHIFT AC/ON (OFF).