Question

please solve this problem

Answer 1

hope this help..........

Answer 2

$Given : \lim_{n \to 1} (\frac{ \sqrt{x^2 - 1}+ \sqrt{x-1} }{ \sqrt{x^3 - 1} } )$

$= \ \textgreater \ \sqrt{ \frac{x^2 - 1}{x^3 - 1} } + \sqrt{ \frac{x - 1}{x^3 - 1} }$

$= \ \textgreater \ \sqrt{ \frac{(x - 1)(x + 1)}{(x - 1)(x^2 + x + 1)} } + \sqrt{ \frac{(x -1)}{(x - 1)(x^2 + x + 1)} }$

$= \ \textgreater \ \sqrt{ \frac{x - 1}{x^2 + x + 1} } + \sqrt{ \frac{1}{x^2 + x + 1} }$

$= \ \textgreater \ \lim_{n \to 1} (\sqrt{ \frac{x + 1}{x^2 + x + 1} } + \sqrt{ \frac{1}{x^2 + x + 1} } )$

$= \ \textgreater \ \sqrt{ \frac{1 + 1}{1 + 1 + 1} } + \sqrt{ \frac{1}{1 + 1 + 1} }$

$= \ \textgreater \ \sqrt{ \frac{2}{3} } + \sqrt{ \frac{1}{3} }$



Hope this helps!