Evaluate $$ \lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{x-1} $$

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Calculate the limit $$ \lim_{x \rightarrow 1} \frac{\sqrt{x}-1}{x-1} $$.
Evaluate the limit by following steps:
- step0: Evaluate using transformations:
  $$\lim _{x\rightarrow 1}\left(\frac{\sqrt{x}-1}{x-1}\right)$$
- step1: Multiply by the Conjugate:
  $$\lim _{x\rightarrow 1}\left(\frac{1}{\sqrt{x}+1}\right)$$
- step2: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 1}\left(1\right)}{\lim _{x\rightarrow 1}\left(\sqrt{x}+1\right)}$$
- step3: Evaluate:
  $$\frac{1}{\lim _{x\rightarrow 1}\left(\sqrt{x}+1\right)}$$
- step4: Evaluate:
  $$\frac{1}{2}$$
The limit of $$ \frac{\sqrt{x}-1}{x-1} $$ as $$ x $$ approaches 1 is $$ \frac{1}{2} $$ or 0.5.
The limit is 0.5.

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