Chapter 9.2, Problem 3QR

To determine

The value of a limit using graphs.

Answer to Problem 3QR

The value of the limit is $1$ .

Explanation of Solution

Given Information: The limit to be calculated is $\underset{x\to 0^{-}}{\lim }{\left(1-\frac{1}{x}\right)}^x$

Method: Plot the graph of the expression in $x$ and identify the value to which the expression approaches as $x$ approaches to $0$ from the left.

The graph of the expression is

  

In the above graph, the expression approaches to $1$ as $x$ approaches to $0$ from the left.

Therefore, the value of the limit is $1$ .