[latex] \lim_{n \to \ 0= \sqrt{x+1} -1/x[/latex]

[latex] \lim_{x \to \ 0} \frac{ \sqrt{x+1}-1 }{x} = \frac{ \sqrt{0+1}-1 }{0} = \frac{0}{0} [/latex] неопределенность 0/0 [latex] \lim_{x \to \ 0} \frac{ \sqrt{x+1} -1}{x} = \lim_{x \to \ 0} \frac{( \sqrt{x+1} -1)*( \sqrt{x+1} +1)}{x*( \sqrt{x+1}+1 )} = \lim_{x \to \ 0} \frac{( \sqrt{x+1} ) ^{2} - 1^{2} }{x*( \sqrt{x+1}+1 )} = [/latex] [latex]= \lim_{x \to \ 0} \frac{x+1-1}{x*( \sqrt{x+1}+1) } = \lim_{x \to \ 0} \frac{x}{x*( \sqrt{x+1}+1 )} = \lim_{x \to \ 0} \frac{1}{ \sqrt{x+1}+1 } = [/latex] [latex]= \frac{1}{ \sqrt{0+1}+1 } = \frac{1}{2}=0,5 [/latex]