l i m x → 2 √ x − 2 + √ x − √ 2 √ x 2 − 4 is equal to Options: A . &nbsp 1/2 B . &nbsp 1 C . &nbsp 2 D . &nbsp -1

Answer: Option A : A = l i m x → 2 { 1 √ x + 2 + √ x − √ 2 √ x 2 − 4 } Limit = 1 2 + l i m x → 2 x − 2 √ x + √ 2 1 √ ( x + 2 ) ( x − 2 ) = 1 2 + l i m x → 2 1 √ x + √ 2 √ x − 2 x + 2 = 1 2

limx→2√x−2+√x−√2√x2−4i

Discussion Forum : Limits Continuity And Differentiability

Question -

$l i m x \to 2 \frac{\sqrt{x - 2} + \sqrt{x} - \sqrt{2}}{\sqrt{x^{2} - 4}} is equal to$

Options:

A . 1/2

B . 1

C . 2

D . -1

Answer: Option A
:
A

$= l i m x \to 2 {\frac{1}{\sqrt{x + 2}} + \frac{\sqrt{x} - \sqrt{2}}{\sqrt{x^{2} - 4}}} Limit = \frac{1}{2} + l i m x \to 2 \frac{x - 2}{\sqrt{x} + \sqrt{2}} \frac{1}{\sqrt{(x + 2) (x - 2)}} = \frac{1}{2} + l i m x \to 2 \frac{1}{\sqrt{x} + \sqrt{2}} \sqrt{\frac{x - 2}{x + 2}} = \frac{1}{2}$

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Discussion Forum : Limits Continuity And Differentiability

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