1. Tardigrade
  2. Question
  3. Mathematics
  4. lim x arrow 3 (√5 x+1-√7 x-5/√7 x+4-√5 x+10)=

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\lim _{x \rightarrow 3} \frac{\sqrt{5 x+1}-\sqrt{7 x-5}}{\sqrt{7 x+4}-\sqrt{5 x+10}}=$

Limits

Solution:

$\lim _{x \rightarrow 3} \frac{\sqrt{5 x+1}-\sqrt{7 x-5}}{\sqrt{7 x+4}-\sqrt{5 x+10}}=\frac{0}{0}$
That is, indeterminate form.
Multiply both the numerator and the denominator with $(\sqrt{5 x+1}+\sqrt{7 x-5})(\sqrt{7 x+4}+\sqrt{5 x+10})$
$\Rightarrow \lim _{x \rightarrow 3} \frac{[5 x+1-(7 x-5)](\sqrt{7 x+4}+\sqrt{5 x+10})}{(7 x+4-5 x-10)(\sqrt{5 x+1}+\sqrt{7 x-5})} $
$ \Rightarrow \lim _{x \rightarrow 3} \frac{(-2 x+6)(\sqrt{7 x+4}+\sqrt{5 x+10})}{(2 x-6)(\sqrt{5 x+1}+\sqrt{7 x-5})} $
$ =\lim _{x \rightarrow 3} \frac{-(\sqrt{7 x+4}+\sqrt{5 x+10})}{(\sqrt{5 x+1}+\sqrt{7 x-5})} $
$ =\frac{-(\sqrt{25}+\sqrt{25})}{(\sqrt{16}+\sqrt{16})}=\frac{-10}{8}=\frac{-5}{4} .$