Biết lim x → 0 (√ 5x + 3 − √ 3)/ x = a/ b √ c ( a , b , c ∈ Z ) Tính a + b − c .

Giải chi tiết:

Ta có:

\[\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {5x + 3} - \sqrt 3 }}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{(5x + 3) - 3}}{{x(\sqrt {5x + 3} + \sqrt 3 )}}\]

  \[ = \mathop {\lim }\limits_{x \to 0} \frac{{5x}}{{x(\sqrt {5x + 3} + \sqrt 3 )}} = \frac{5}{{2\sqrt 3 }}\]

Suy ra:

                                                 \[a = 5,\quad b = 2,\quad c = 3\]

                                                      \[a + b - c = 5 + 2 - 3 = 4\]

Đáp án: D.