# Chapter 2 - Limits - 2.8 Intermediate Value Theorem - Preliminary Questions - Page 86: 1

The result follows by the Intermediate Value Theorem.

#### Work Step by Step

Since the function $x^2$ is continuous on $[0,1]$ and $f(0)=0\neq f(1)=1$, thus $0.5$ is between $f(0)$ and $f(1)$. Then, by the Intermediate Value Theorem, the function $x^2$ takes the value $0.5$ for some $x\in (0,1)$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.