Question

limit extends to 2 x square - 7 x minus 4 by 2 x minus 1 into root x minus 2

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \lim_{x \to 2} \: \frac{2 {x}^{2} - 7x - 4 }{(2x - 1) (\sqrt{x } - 2) } }$

EVALUATION

$\displaystyle \sf{ \lim_{x \to 2} \: \frac{2 {x}^{2} - 7x - 4 }{(2x - 1) (\sqrt{x } - 2) } }$

$\displaystyle \sf{ = \lim_{x \to 2} \: \frac{2 {x}^{2} - 8x + x - 4 }{(2x - 1) (\sqrt{x } - 2) } }$

$\displaystyle \sf{ = \lim_{x \to 2} \: \frac{(2x + 1)(x - 4) }{(2x - 1) (\sqrt{x } - 2)} }$

$\displaystyle \sf{ = \lim_{x \to 2} \: \frac{(2x + 1)( \sqrt{x} + 2)( \sqrt{x} - 2) }{(2x - 1) (\sqrt{x } - 2)} }$

$\displaystyle \sf{ = \lim_{x \to 2} \: \frac{(2x + 1)( \sqrt{x} + 2) }{(2x - 1)} }$

$\displaystyle \sf{ = \frac{(4 + 1)( \sqrt{2} + 2)}{(4 - 1) } }$

$\displaystyle \sf{ = \frac{5}{3} (2 + \sqrt{2} ) }$

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