Explanation

(d)
$\lim_{x \rightarrow \infty}\frac{(2x - 3)(3x - 4)}{(4x - 5)(5x - 6)} = \lim_{x \rightarrow \infty}\frac{6x^{2} - 17x + 12}{20x^{2} - 49x + 30}$
$= \lim_{x \rightarrow \infty}\frac{12x - 17}{40x - 49}$ [using L’ Hospital’s rule]
$= \lim_{x \rightarrow \infty}{\frac{12}{40} = \frac{3}{10}}$ [using L’ Hospital’s rule]