Trigonometry Workbook For Dummies
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Solving for limits at infinity is easy to do when you use a calculator. For example, enter the below function in your calculator's graphing mode:


then go to table setup and set TblStart to 100,000 and ∆Tbl to 100,000.

The table below shows the results.

X y
100,000 .4999988
200,000 .4999994
300,000 .4999996
400,000 .4999997
500,000 .4999998
600,000 .4999998
700,000 .4999998
800,000 .4999998
900,000 .4999999

You can see that y is getting extremely close to 0.5 as x gets larger and larger. So, 0.5 is the limit of the function as x approaches positive infinity, and there’s a horizontal asymptote at y = 0.5.

If you have any doubt that the limit equals 0.5, go back to table setup and put in a humongous TblStart and ∆Tbl, say 1,000,000,000, and check the table results again. All you see is a column of 0.5s. That’s the limit.

(By the way, the limit of this function as x approaches negative infinity doesn’t equal the limit as x approaches positive infinity:


One more thing: Just as with regular limits, using a calculator for infinite limits won’t give you an exact answer unless the numbers in the table are getting close to a number you recognize, like 0.5. If, for example, the exact answer to the limit is something like 5/17, which equals 0.2941…, when you see values in the table getting close to 0.2941, you probably won’t know that the values are approaching 5/17. You will, however, at least have an approximate answer to the limit problem.

Substitution does not work for the problem you solved above,


If you plug ∞ into x, you get ∞ – ∞, which does not equal zero. A result of ∞ – ∞ tells you nothing about the answer to a limit problem.

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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