_ x - (2 x-3)(3 x-4) (4 x-5)(5 x-6) = - Vidyadip

MCQ

$\lim _{x \rightarrow-\infty} \frac{(2 x-3)(3 x-4)}{(4 x-5)(5 x-6)}=$

A
$0$
B
$\frac{1}{10}$
C
$\frac{1}{5}$
✓
$\frac{3}{10}$

✓

Answer

Correct option: D.

$\frac{3}{10}$

(D)
$\lim _{x \rightarrow \infty} \frac{(2 x-3)(3 x-4)}{(4 x-5)(5 x-6)}=\lim _{x \rightarrow \infty} \frac{x\left(2-\frac{3}{x}\right) x\left(3-\frac{4}{x}\right)}{x\left(4-\frac{5}{x}\right) x\left(5-\frac{6}{x}\right)}$
$=\frac{(2-0)(3-0)}{(4-0)(5-0)}$
$=\frac{6}{20}=\frac{3}{10}$

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