Question

lim x tends to infinity √x+1-√x
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Answer 1

Step-by-step explanation:

We have,

$\displaystyle \tt{ \lim_{x \to \infty} \left( \sqrt{x + 1} - \sqrt{x} \right)}$

$\displaystyle \tt{ = \lim_{x \to \infty} \dfrac{ \left( \sqrt{x + 1} - \sqrt{x} \right) \left( \sqrt{x + 1} + \sqrt{x} \right)}{ \left( \sqrt{x + 1} + \sqrt{x} \right)}}$

$\displaystyle \tt{ = \lim_{x \to \infty} \dfrac{ x + 1- x }{ \sqrt{x + 1} + \sqrt{x} }}$

$\displaystyle \tt{ = \lim_{x \to \infty} \dfrac{ 1 }{ \sqrt{x + 1} + \sqrt{x} }}$

$\displaystyle \tt{ = \dfrac{ 1 }{ \infty }}$

$\displaystyle \tt{ = 0}$

Answer 2

Step-by-step explanation:

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