Câu hỏi
Tính \(\mathop {\lim }\limits_{x \to 2} \frac{{{x^3} - 6{x^2} + 11x - 6}}{{{x^2} - 4}}\)bằng?
- A \(\frac{1}{4}.\)
- B \(\frac{1}{3}.\)
- C \( - \frac{1}{4}.\)
- D \( - \frac{1}{3}.\)
Lời giải chi tiết:
\(\mathop {\lim }\limits_{x \to 2} \frac{{{x^3} - 6{x^2} + 11x - 6}}{{{x^2} - 4}} = \mathop {\lim }\limits_{x \to 2} \frac{{(x - 1)(x - 2)(x - 3)}}{{(x - 2)(x + 2)}} = \mathop {\lim }\limits_{x \to 2} \frac{{(x - 1)(x - 3)}}{{x + 2}} = \frac{{(2 - 1)(2 - 3)}}{{2 + 2}} = \frac{{ - 1}}{4}\)
Chọn: C.
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