Cho hàm số \(f\left( x \right) = \frac{{\sqrt {{x^...

Câu hỏi: Cho hàm số $f\left( x \right) = \frac{{\sqrt {{x^2} + 3{a^2}}  - 2a}}{{x - a}} + a$, (với $a > 0,\,\,a$ là tham số). Tính $\mathop {\lim }\limits_{x \to a} f\left( x \right).$

A. $\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{{2a - 1}}{2}.$

B. $\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{{2a + 1}}{2}.$

C. $\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{2}{{2a + 1}}.$

D. $\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{2}{{2a - 1}}.$