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

[tex] \lim_{x \to \ 4} \frac{ \sqrt{x} -2}{x-4} = \frac{ \sqrt{4}-2 }{4-4} = \frac{0}{0} [/tex]
неопределенность 0/0
[tex] \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)} = [/tex]
[tex]= \lim_{x \to \ 4} \frac{1}{ \sqrt{x} +2} = \frac{1}{ \sqrt{4}+2 } = \frac{1}{4}=0,25 [/tex]