Question

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$lim_{x to 1} frac{ x^{2} -1}{ sqrt{x} -1}$

Answer 1

$lim_{x to 1} frac{ x^{2} -1}{ sqrt{x} -1} =frac{0}{0}= lim_{x to 1} frac{ (x-1)(x+1)}{ sqrt{x} -1} =lim_{x to 1} frac{ (x-1)(x+1)}{ sqrt{x} -1}=\=lim_{x to 1} frac{ (sqrt x-1)(sqrt x+1)(x+1)}{ sqrt{x} -1}=lim_{x to 1} (sqrt x+1)(x+1)=4$