Chapter 2.1, Problem 38E

To determine

To find: The value of $\underset{x\to 0^{-}}{\lim }\left(\mathrm{int}x\right)$ .

Answer to Problem 38E

The value of $\underset{x\to 0^{-}}{\lim }\left(\mathrm{int}x\right)$ is $-1$ .

Explanation of Solution

Given information: The limit is $\underset{x\to 0^{-}}{\lim }\left(\mathrm{int}x\right)$ .

Calculation:

The limit $\underset{x\to 0^{-}}{\lim }\left(\mathrm{int}x\right)$ is the approach of $x=0$ from the left hand side.

The function $\mathrm{int}x$ is piecewise function and the value of $\mathrm{int}x$ is $-1$ for all $x$ in $\left[-1,0\right)$ . So, the value of $\mathrm{int}x$ at $x=0$ approached from left side is $-1$ .

Therefore, the value of $\underset{x\to 0^{-}}{\lim }\left(\mathrm{int}x\right)$ is $-1$ .