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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.2, Problem 25E

(a)

To determine

The value of *y*-axis.

Expert Solution

The value of

Using the online graphing calculator and draw the graph of the function

Zoom in the graph towards the point where the graph crosses the *y*-axis as shown below in Figure 2.

From Figure 2, it is observed that graph of *x* approaches 0 from either side.

That is,

Since the right hand limits and the left hand limits are equal, the value of

Thus, the value of

(b)

To determine

The answer obtained in part (a) by evaluating the value of *x* approaches 0.

Expert Solution

The value of

As *x* approaches 0, evaluate the function

Evaluate the function (correct to 6 decimal places) for the values of *x* and get the following table of values.

−0.5 | −0.337280 | 0.25 | −1.349121 |

−0.1 | −0.014937 | 0.01 | −1.493758 |

−0.01 | −0.000149 | 0.0001 | −1.499937 |

−0.001 | −0.0000015 | 0.000001 | −1.499999 |

−0.0001 | −0.000000015 | 0.00000001 | −1.499999 |

0.5 | −0.337280 | 0.25 | −1.349121 |

0.1 | −0.014937 | 0.01 | −1.493758 |

0.01 | −0.000149 | 0.0001 | −1.499937 |

0.001 | −0.0000015 | 0.000001 | −1.499999 |

0.0001 | −0.000000015 | 0.00000001 | −1.499999 |

Here, it is observed that the value of *x* approaches to 0 from the either side. That is,

Therefore, it is verified from the table that