SITE-C teams: Lesson 7

Investigate graphically the following limit:

lim x-> -0.4 ( 5 x + 2 ) / ( 5 x^{2} - 13 x - 6 )

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 ( 5 x + 2 ) ¸
( 5 x^{2} - 13 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 = -0.4. Let’s zoom in on that hole by zooming in with a box the top left-hand corner of which is (-0.5, -0.2) and the bottom right-hand corner of which is (-0.3, -0.4).

Press **SHIFT** **F2** (ZOOM) **F1** (BOX), use the cursor arrows to move to x = -0.5 and y = -0.2, and press **EXE** to mark the top left-hand corner of the box. Continue to use the cursor arrows to move to x = -0.3 and y = -0.4, 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 = -0.4015873015 and y = -0.29398040013. The first point displayed on the right-hand side of the hole is x = -0.3984126984 and y = -0.294255021. From this information, it is reasonable to conclude that the limit is about -0.294.

Press **SHIFT** **F5** (G-Solv) **F6** ( |> ) **F1** (Y-CAL), enter -0.4 at the X= prompt, and press **EXE**. Note that the calculator’s 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. The last point displayed before a jump from a negative to a positive y-value is x = 2.9 and y = -10. The first point displayed after the jump is x = 3.1 and y = 10. This indicated that there is an asymptote at x = 3.

Press **SHIFT** **F5** (G-Solv) **F6** ( |> ) **F1** (Y-CAL), enter 3 at the X= prompt, and press **EXE**. Note that the calculator’s response is __Not Found__.

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

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