Question

Examine the continuity of the function f(x) = 2x2-1 at x = 3.

Answer 1

The given function is f(x) = 2x2-1
At x = 3, f(x) = f(3) = 2x32-1 = 17
$\lim\limits_{x \to 3}$ f(x) = $\lim\limits_{x \to 3}$ (2x2-1) = 2x32-1 = 17
∴$\lim\limits_{x \to 3}$ f(x) = f(3)

Therefore, f is continuous at x=3.