Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises - Page 124: 21

Since $~~\lim\limits_{x \to 0}f(x) \neq f(0)$, the function is not continuous at $x = 0$

$f(0) = 0$ $\lim\limits_{x \to 0^-}f(x) = cos(0)= 1$ $\lim\limits_{x \to 0^+}f(x) = 1-(0)^2= 1$ $\lim\limits_{x \to 0}f(x) = 1$ Note that $\lim\limits_{x \to 0}f(x) \neq f(0)$ Since $~~\lim\limits_{x \to 0}f(x) \neq f(0)$, the function is not continuous at $x = 0$