1. Tardigrade
  2. Question
  3. Mathematics
  4. Find the limit of displaystyle lim x arrow ∞ ((x-5)(x-4)/(2 x-3)(x-7))

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Find the limit of $\displaystyle\lim _{x \rightarrow \infty} \frac{(x-5)(x-4)}{(2 x-3)(x-7)}$

Limits

Solution:

$\displaystyle\lim _{x \rightarrow \infty} \frac{(x-5)(x-4)}{(2 x-3)(x-7)} =\displaystyle\lim _{x \rightarrow \infty} \frac{x^2-9 x+20}{2 x^2-17 x+21}$
$ =\displaystyle\lim _{x \rightarrow \infty} \frac{1-\frac{9}{x}+\frac{20}{x^2}}{2-\frac{17}{x}+\frac{21}{x^2}}=\frac{1}{2}$