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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.2, Problem 19E

To determine

**To guess:** The value of

Expert Solution

The limit of the function is guessed to 5.

**Given:**

The values of *t* are

**Calculation:**

Since *t* approaches 0, the values

Evaluate the function (correct to 6 decimal places) when

−0.5 | 0.082084999 | −0.91792 | 1.835830 |

−0.1 | 0.60653066 | −0.39347 | 3.934693 |

−0.01 | 0.951229425 | −0.04877 | 4.877057 |

−0.001 | 0.995012479 | −0.00499 | 4.987520 |

−0.0001 | 0.999500125 | −0.0005 | 4.998750 |

Here, the value of *t* approaches 0 from the left side.

That is,

Evaluate the function (correct to 6 decimal places) when

0.5 | 12.18249396 | 11.18249 | 22.364987 |

0.1 | 1.648721271 | 0.648721 | 6.487212 |

0.01 | 1.051271096 | 0.051271 | 5.127109 |

0.001 | 1.005012521 | 0.005013 | 5.012520 |

0.0001 | 1.000500125 | 0.0005 | 5.001250 |

Here, the value of *t* approaches 0 from the right side.

That is,

Since the right hand limit and the left hand limits are the same,

Therefore, the limit of the function is guessed to 5.