SITE-C teams: Lesson 8

 

Investigate graphically the following limit:

lim x-> -2 ( x + 2 ) / ( 2 x2 + 7 x + 6 )

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 ( x + 2 ) ¸ ( 2 x2 + 7 x + 6 ) and press EXE to store it in memory.

Press SHIFT and F3 (V-Window) to enter the viewing window screen, and press F1 (INIT) to select the initial viewing window parameters.

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.

A hole is clearly visible at x = -2. Letís zoom in on that hole by zooming in with a box the top left-hand corner of which is (-2.1, -0.7) and the bottom right-hand corner of which is (-1.9, -1.3).

Press SHIFT F2 (ZOOM) F1 (BOX), use the cursor arrows to move to x = -2.1 and y = -0.7, and press EXE to mark the top left-hand corner of the box. Continue to use the cursor arrows to move to x = -1.9 and y = -1.3, and press EXE.

Press SHIFT F1 (Trace) and use the right cursor arrow to approach the hole. The last point displayed on the left-hand side of the hole is x = -2.0015873015 and y = -0.996835443. The first point displayed on the right-hand side of the hole is x = -1.9984126984 and y = -1.0031847133. From this information, it is reasonable to conclude that the limit is about -1.0.

Press SHIFT F5 (G-Solv) F6 ( |> ) F1 (Y-CAL), enter -2 at the X= prompt, and press EXE. Note that the calculatorís response is Not Found.

Press SHIFT F2 (ZOOM) F6 ( |> ) F1 (ORIG) to return to the original view window and drawing. Press SHIFT F5 (G-Solv) F4 (Y-ICPT) to obtain the y-intercept which is 0.333333...

Press SHIFT F1 (Trace) and use the right cursor arrow to approach x = - 3/2. The last point displayed before a jump from a negative to a positive y-value is x = -1.6 and y = -5. The first point displayed after the jump is x = -1.4 and y = 5. This indicated that there is an asymptote at x = - 3/2.

Press SHIFT F5 (G-Solv) F6 ( |> ) F1 (Y-CAL), enter -1.5 at the X= prompt, and press EXE. Note that the calculatorís response is Not Found.

Press EXIT MENU.

Turn off the CASIO CFX-9850G by pressing SHIFT AC/ON (OFF).