Advertisements (Quảng cáo)
Cho hàm số
\(f\left( x \right) = \left\{ \matrix{
\sqrt {9 – {x^2}} \text{ với } – 3 \le x < 3 \hfill \cr
1\text{ với }x = 3 \hfill \cr
\sqrt {{x^2} – 9} \text{ với }x > 3. \hfill \cr} \right.\)
Tìm \(\mathop {\lim }\limits_{x \to {3^ + }} f\left( x \right),\mathop {\lim }\limits_{x \to {3^ – }} f\left( x \right),\) và \(\mathop {\lim }\limits_{x \to 3} f\left( x \right)\) (nếu có).
\(\mathop {\lim }\limits_{x \to {3^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to {3^ + }} \sqrt {{x^2} – 9} = 0;\)
Advertisements (Quảng cáo)
\(\mathop {\lim }\limits_{x \to {3^ – }} f\left( x \right) = \mathop {\lim }\limits_{x \to {3^ – }} \sqrt {9 – {x^2}} = 0.\)
Do đó
\(\mathop {\lim }\limits_{x \to 3} f\left( x \right) = 0.\)