# Examine the continuity of the function.

Question:

Examine the continuity of the function $f(x)=2 x^{2}-1$ at $x=3$.

Solution:

The given function is $f(x)=2 x^{2}-1$

At $x=3, f(x)=f(3)=2 \times 3^{2}-1=17$

$\lim _{x \rightarrow 3} f(x)=\lim _{x \rightarrow 3}\left(2 x^{2}-1\right)=2 \times 3^{2}-1=17$

$\therefore \lim _{x \rightarrow 3} f(x)=f(3)$

Thus, f is continuous at x = 3