Question

evaluate this expression.

Answer 1

$\lim_{n \to 0} ( \frac{ \sqrt{1 + x} - \sqrt{1-x} }{x} )$

= > $\frac{( \sqrt{1 + x} - \sqrt{1 - x}) * ( \sqrt{1 + x} + \sqrt{1 - x} ) }{x( \sqrt{1 + x} + \sqrt{1 - x}) }$

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

= > $\frac{1 + x - 1 + x}{x( \sqrt{1 + x} + \sqrt{1 - x}) }$

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

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

Now,

$\lim_{n \to 0} ( \frac{2}{ \sqrt{1 + x} + \sqrt{1 - x} } )$

$= \ \textgreater \ \frac{2}{ \sqrt{1 + 0} + \sqrt{1 - 0} }$

$= \ \textgreater \ \frac{2}{2}$

= > 1.



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks