Tìm giới hạn \(B = \mathop {\lim }\limits_{x \to 1} \frac{{\sqrt {4x + 5} - 3}}{{\sqrt[3]{{5x + 3}} - 2}}\)

* Hướng dẫn giải

\(\begin{array}{l}
B = \mathop {\lim }\limits_{x \to 1} \frac{{\sqrt {4x + 5}  - 3}}{{\sqrt[3]{{5x + 3}} - 2}} = \mathop {\lim }\limits_{x \to 1} \frac{{4\left( {x - 1} \right)\left[ {\sqrt[3]{{{{\left( {5x + 3} \right)}^2}}} + 2\sqrt[3]{{5x + 3}} + 4} \right]}}{{5\left( {x - 1} \right)\left( {\sqrt {4x + 5}  + 3} \right)}}\\
 = \mathop {\lim }\limits_{x \to 1} \frac{{4\left[ {\sqrt[3]{{{{\left( {5x + 3} \right)}^2}}} + 2\sqrt[3]{{5x + 3}} + 4} \right]}}{{5\left( {\sqrt {4x + 5}  + 3} \right)}} = \frac{2}{5}
\end{array}\)