Chapter 11, Problem 4CR

To determine

To evaluate: the limit using table and determine whether limit can be reached.

Answer to Problem 4CR

  $\underset{x\to 0}{\lim }\frac{\ln \left(1-x\right)}{x}=-1$

Explanation of Solution

Given:

  $\underset{x\to 0}{\lim }\frac{\ln \left(1-x\right)}{x}$

It is given that,

  $\underset{x\to 0}{\lim }\frac{\ln \left(1-x\right)}{x}$

Making the table to evaluate the limit when ‘ x’ tends to 0,

x	f ( x )
−0.1	−0.953
−0.09	−0.957
−0.01	−0.995
−0.001	−0.9995
−0.0001	−0.99995

So, it can be seen from the table when x approaches 0, f ( x ) approaches −1.

Hence,

  $\underset{x\to 0}{\lim }\frac{\ln \left(1-x\right)}{x}=-1$