# How to Solve Limits at Infinity with a Calculator

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 *t**able **s**etup *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 *t**able **s**etup* 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.