Question

please tell me correct answer of this and take brainalist mark​

Answer 1

Step-by-step explanation:

We have,

$\lim _{x \rarr2 } \frac{ (\sqrt{1 + 2x - {x}^{2} } )- (x - 1)}{x - 2}$

$= \lim _{x \rarr2 } \frac{(( \sqrt{1 + 2x - {x}^{2} } ) - (x - 1))(( \sqrt{1 + 2x - {x}^{2} }) + (x - 1)) }{(x - 2)(( \sqrt{1 + 2x - {x}^{2} }) + (x - 1) )}$

$= \lim _{x \rarr2 } \frac{1 + 2x - {x}^{2} - {x}^{2} + 2x - 1 }{(x - 2)(( \sqrt{1 + 2x - {x}^{2} }) + (x + 1)) }$

$= \lim _{x \rarr2 } \frac{ -2x(x - 2) }{(x - 2)(( \sqrt{1 + 2x - {x}^{2} } ) + (x - 1))}$

$= \lim _{x \rarr2 } \frac{ - 2x}{( \sqrt{1 + 2x - {x}^{2} }) + (x - 1) }$

$= \frac{ - 2 \times2 }{ \sqrt{1 + 4 - 4} + 2 - 1 }$

$= \frac{ -4 }{2}$

$= - 2$