3.5 Notes Evaluating limits x approaches positive or negative infinity

3.5 Notes In addition to limits where x approaches a number, there are limits where x approaches infinity (or negative infinity). A limit as x is approaching infinity (or negative infinity) is asking what f(x) is getting close to as x is getter larger and larger.

3.5 Notes In today’s do now assignment you were actually evaluating a limit where x approaches infinity. As larger and larger values are x were evaluated in the function provided, the f(x) values got closer and closer to one half. Although f(x) will never reach one half, the limit is equal to one half.

3.5 Notes Just like a graphing calculator’s table feature was used to evaluate limits as x approached a number, it can be used to evaluate limits as x approaches infinity. However, rather than setting up the table to simulate x jumping by small increments to get close to some number, the table is set up to simulate x approaching infinity.

3.5 Notes The function’s equation is typed in on the Y= screen as before. In the Table Setup menu we were starting the table (TblStart) at the value x is approaching and choosing a small number for the increment (ΔTbl) by which the x values changed. How should the menu be set up to simulate approaching infinity? By choosing relatively large numbers for both the TblStart and the ΔTbl.

3.5 Notes Consider today’s do now assignment again: Go to the Y= screen and type in the function.

3.5 Notes Press 2 nd and WINDOW (TBL SET) to bring up the “Table Setup Menu.” Start the table at some large value, say 10, and set the increment (∆ Tbl) to some large value, say 50.

3.5 Notes Press 2 nd and GRAPH (TABLE) to view the table.

3.5 Notes Scrolling further down the table reveals that.5 appears in the y column. Realize however, that because the Y column only has five decimal places, the calculator is rounding. The f(x) values get very close to but never actually reach it.

3.5 Notes Another example… Type the equation on the Y= screen.

3.5 Notes Choose large numbers in the Table Setup Menu. This time 50 is chosen for TblStart and 100 for ΔTbl.

3.5 Notes View the t-table: As you scroll up the table (simulating x approaching negative infinity) the y values appear to be getting closer to -.5.

3.5 Notes Another example… Type the equation on the Y= screen.

3.5 Notes Make sure the calculator is in radian mode since the limit is of a trigonometric function. Choose large numbers in the Table Setup Menu. This time 100 is chosen for both TblStart and ΔTbl.

3.5 Notes View the t-table: As you scroll down the table (simulating x approaching infinity) the y values appear to be getting closer to 0.

3.5 Notes One more example… Type the equation on the Y= screen.

3.5 Notes Set up the table. This time 100 is being used for both TblStart and ΔTbl.

3.5 Notes Notice as you look down the values in the y column that they are getting larger and larger rather than approaching some value. The y values are also approaching infinity.

3.5 Notes As x is approaching infinity, f(x) is approaching infinity. Therefore, the limit does not exist.

3.5 Notes – Practice Problems: