Question

$\displaystyle\lim_{x \to \infty} \frac{ (2x -3)(3x -4)}{(4x - 5)(5x - 6)}$ is equal to:

• A. $\frac{1}{10}$
• B. 0
• C. $\frac{1}{5}$
• D. $\frac{3}{10}$

Answer 1

Answer: (D)

$\frac{3}{10}$

Answer 2

Let $f(x) = \frac{ (2x -3)(3x -4)}{(4x - 5)(5x - 6)}$ we have to find $\displaystyle\lim_{x \to \infty} f(x)$ Put $x = \frac{1}{h},$ if $x \to \infty ,h \to 0$ then $\displaystyle\lim_{x \to \infty} f(x) = \displaystyle\lim_{h \to 0} \frac{ (2x -3h)(3x -4h)}{(4x - 5h)(5x - 6h)}$ $= \frac{6}{20} = \frac{3}{10}$