Question

please evaluate and help me​

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr \infty } \sqrt{x} (\sqrt{x + 3} - \sqrt{x} )$

$\lim _{x \rarr \infty } \frac{ \sqrt{x}(x + 3 - x) }{( \sqrt{x + 3} + \sqrt{x} )}$

$= \lim_{x \rarr \infty } \frac{3 \sqrt{x} }{ \sqrt{x + 3} + \sqrt{x} }$

$= \lim_{x \rarr \infty } \frac{3}{ \sqrt{ 1 + \frac{3}{x} } + 1 }$

$= \frac{3}{1 + 1}$

$= \frac{3}{2}$