Explanation

(c)
$\lim_{x \rightarrow \infty}\frac{(2x + 1)^{40}(4x - 1)^{5}}{(2x + 3)^{45}} = \lim_{x \rightarrow \infty}\frac{{x^{40}\left( 2 + \frac{1}{x} \right)}^{40}{x^{5}\left( 4 - \frac{1}{x} \right)}^{5}}{x^{45}\left( 2 + \frac{3}{x} \right)^{45}}$
$= \frac{(2 + 0)^{40}(4 - 0)^{5}}{(2 + 0)^{45}} = \frac{2^{50}}{2^{45}} = 32$