Question

$\lim_{x \to \ 1} \frac{\sqrt{x} -1}{x-1}$ calcule o limite quando x tende a 1.

Answer 1

$\mathsf{x-1=(\sqrt{x} +1)(\sqrt{x}-1)}$

$\mathsf{\lim_{x \to \ 1} \dfrac{\sqrt{x} -1}{x-1}}$

$\mathsf{\lim_{x \to \ 1} \dfrac{\cancel{\sqrt{x} -1}}{(\sqrt{x} +1)(\cancel{\sqrt{x}-1)}}}$

$\mathsf{\lim_{x \to \ 1} \dfrac{1}{(\sqrt{x} +1)}}$

$\mathsf{\lim_{x \to \ 1} \dfrac{1}{(\sqrt{x} +1)}=\dfrac{1}{\sqrt{1}+1}=\dfrac{1}{2}}$