(a) Use numerical and graphical evidence to guess the value of the limit lim xl1 x3 2 1 sx 2 1 (b) How close to 1 does x have to be to ensure that the function in part (a) is within a distance 0.5 of its limit?

Problem 55

a) Use numerical and graphical evidence to guess the value of the limit

b) How close to 1 does x have to be in order to ensure that the function in part a is within 0.5 of its limit?

Step by Step Solution

Step 1 of 3

(a)

Make a table of values for the function shown below:

x |
f(x) |

0.9 |
5.280931738 |

0.99 |
5.925312187 |

0.999 |
5.992503125 |

0.9999 |
5.999250031 |

1.0001 |
6.000750031 |

1.001 |
6.007503125 |

1.01 |
6.075312812 |

1.1 |
6.781557287 |