Question

heya mate solve it...

Answer 1

$lim \: \: \: \: \frac{ \sqrt{x + h} - \sqrt{x} }{h} \\ h = 0$

Now, Rationalise the Numerator.


$lim \: \: \: \: \: \: \: \: \frac{( \sqrt{x + h} - \sqrt{x} \: )( \: \sqrt{x + h} + \sqrt{x} \: ) }{h( \sqrt{x + h} + \sqrt{x} } \\ h = 0$




$lim \: \: \: \: \: \: \: \: \: \frac{ {( \: \sqrt{x + h} )}^{2} - {( \: \sqrt{x} )}^{2} }{h( \sqrt{x + h} + \sqrt{x} } \\ h = 0$



$lim \: \: \: \: \: \: \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x} )} \\ h = 0$




$lim \: \: \: \: \: \: \: \: \: \: \: \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } \\ h = 0$







$lim \: \: \: \: \: \: \: \: \: \: \frac{1}{\: ( \: \sqrt{x + h} \: + \: \sqrt{x} \: )} \\ h = 0$




Now, Substitute the value of h ---- 0


$\frac{1}{ \sqrt{x + 0} + \sqrt{x} } \\ \\ \\ = \: \frac{1}{ \sqrt{x} + \sqrt{x} } \\ \\ \\ = \: \frac{1}{2 \sqrt{x} } ..............is \: the \: answer \: of \: your \: question.$




$\\ \\ \\ hope \: this \: will \: help \: you............... \\ \\ \\ \\ \\ \\ be \: brainly................$






☛ ⛧⛧ By, Ⓜr. Thakur ⛧⛧