Cho lìm(x)-10/x-1=5. Giá trị lìm(x)-10/(căn x-1)(căn 4f(x)+9+3 bằng bao nhiêu

\(\mathop {\lim }\limits_{x \to 1} \frac{{f(x) - 10}}{{x - 1}} = 5\) nên  hay

Do đó \(\mathop {\lim }\limits_{x \to 1} \frac{{f(x) - 10}}{{\left( {\sqrt x  - 1} \right)\left[ {\sqrt {4f(x) + 9}  + 3} \right]}} = \mathop {\lim }\limits_{x \to 1} \frac{{5x + 5 - 10}}{{\left( {\sqrt x  - 1} \right)\left[ {\sqrt {4\left( {5x + 5} \right) + 9}  + 3} \right]}}\)

\[ = \mathop {\lim }\limits_{x \to 1} \frac{{5\left( {x - 1} \right)\left( {\sqrt x  + 1} \right)}}{{\left( {x - 1} \right)\left( {\sqrt {20x + 29}  + 3} \right)}} = \mathop {\lim }\limits_{x \to 1} \frac{{5\left( {\sqrt x  + 1} \right)}}{{\sqrt {20x + 29}  + 3}} = 1\].

Đáp án: 1.