Chapter 11, Problem 5CR

To determine

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

Answer to Problem 5CR

  $\underset{x\to 1}{\lim }\left(3-x\right)=2$

Explanation of Solution

Given:

  $\underset{x\to 1}{\lim }\left(3-x\right)$

It is given that,

  $\underset{x\to 1}{\lim }\left(3-x\right)$

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

x	f ( x )
0.8	2.2
0.9	2.1
0.99	2.01
0.999	2.001
0.9999	2.0001

So, it can be seen from the table when x approaches 1, f ( x ) approaches 2.

Hence,

  $\underset{x\to 1}{\lim }\left(3-x\right)=2$