Cho hàm số \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{\dfrac{{\sqrt {2{x^2} + 8} - x - 2}}{{{x^2} - 4}}\,\,\,khi\,\,x < 2}\\{\,\,\,\dfrac{{\sin \left( {x - 2} \right)}}{{{x^2} - 3x + 2}}\,\,\,\,\,\,\,\,\,\,khi\,\,x > 2}\end{array}} \right.\). Tìm\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right),\mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right)\) và \(\mathop {\lim }\limits_{x \to 2} f\left( x \right)\) nếu có.
A.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = 1,\,\,\mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = 0\) và \(\mathop {\lim }\limits_{x \to 2} f\left( x \right)\) không tồn tại.
B.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = 1,\,\,\mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = \dfrac{1}{2}\) và \(\mathop {\lim }\limits_{x \to 2} f\left( x \right)\) không tồn tại.
C.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to 2} f\left( x \right) = 1\).
D.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to 2} f\left( x \right) = 0\).
A.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = 1,\,\,\mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = 0\) và \(\mathop {\lim }\limits_{x \to 2} f\left( x \right)\) không tồn tại.
B.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = 1,\,\,\mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = \dfrac{1}{2}\) và \(\mathop {\lim }\limits_{x \to 2} f\left( x \right)\) không tồn tại.
C.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to 2} f\left( x \right) = 1\).
D.\(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to 2} f\left( x \right) = 0\).
Loga
Hóa Học lớp 12
