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

Answer

Given: $f\left( x \right) = 2{x^2} - 1$ 

Continuity at x = 3 $\mathop {\lim }\limits_{x \to 3} f\left( x \right) = \mathop {\lim }\limits_{x \to 3} \left( {2{x^2} - 1} \right) = 2{\left( 3 \right)^2} - 1 = 18 - 1 = 17$

And $f\left( 3 \right) = 2{\left( 3 \right)^2} - 1 = 18 - 1 = 17$

Since $\mathop {\lim }\limits_{x \to 3} f\left( x \right) = f\left( x \right),$ therefore, f(x) is continuous at x = 3.

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