Examine whether the function f given by f(x) = x2 is continuous a… - Vidyadip

Question

Examine whether the function f given by f(x) = x² 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} $ x² = 0² = 0
Thus $\mathop {\lim }\limits_{x \to 0} f(x)$ = 0 = f (0)
Hence, f is continuous at x = 0.

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