Question

lim x —> 0, x / √a+x - √a-x​

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr0 } \frac{x}{ \sqrt{a + x} - \sqrt{a - x} }$

$\implies\lim_{x \rarr0 } \frac{x( \sqrt{a + x} + \sqrt{a - x} ) }{a + x - a + x}$

$\implies\lim_{x \rarr0 } \frac{x( \sqrt{a + x} + \sqrt{a - x}) }{2x}$

$\implies\lim_{x \rarr0 } \frac{ \sqrt{a + x} + \sqrt{a - x} }{2}$

$= \frac{ \sqrt{a + 0} + \sqrt{a - 0} }{2}$

$= \frac{2 \sqrt{a} }{2}$

$= \sqrt{a}$