Chapter 2.1, Problem 37E

To determine

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

Answer to Problem 37E

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

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 right hand side.

The function $\mathrm{int}x$ is piecewise function and the value of $\mathrm{int}x$ is $0$ for all $x$ in the interval $\left[0,1\right)$ .

So, the value of $\mathrm{int}x$ at $x=0$ approached from right side is $0$ .

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