Examine whether the function f given by f(x) = x^2 is continuous … - Vidyadip

Question

Examine whether the function f given by $f(x) = x^2$ is continuous at $x = 0.$

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Answer

First, note that the function is defined at the given point $x = 0$ and $f(0) = 0$.
Now,
$\mathop {\lim }\limits_{x \to 0} f(x) = \mathop {\lim }\limits_{x \to 0} x^2 = 0^2 = 0$
Thus $\mathop {\lim }\limits_{x \to 0} f(x) = 0 = f (0)$
Hence, $f$ is continuous at $x = 0.$

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