Question

$lim_{x[tex] lim_{x to 4 frac{sqrt{x}-2 }{x-4} [tex] lim_{x to 4} frac{ sqrt{x}-2 }{x-4}$
Решить лимиты.

Answer 1

$lim_{x to 4} frac{ sqrt{x} -2}{x-4} = frac{ sqrt{4}-2 }{4-4} = frac{0}{0}$
неопределенность 0/0
$lim_{x to 4} frac{ sqrt{x} -2}{x-4} = lim_{x to 4} frac{ sqrt{x} -2}{ ( sqrt{x} )^{2} - 2^{2} } = lim_{x to 4} frac{ sqrt{x} -2}{( sqrt{x} -2)*( sqrt{x} +2)} =$
$= lim_{x to 4} frac{1}{ sqrt{x} +2} = frac{1}{ sqrt{4}+2 } = frac{1}{4}=0,25$