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3.5 Notes Evaluating limits x approaches positive or negative infinity

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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.

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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.

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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.

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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.

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

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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.

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

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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.

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

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

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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.

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

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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.

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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.

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

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

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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.

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

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3.5 Notes – Practice Problems: 1. 2. 3. 4.

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