Question

Evaluate

Answer 1

Answer:

  -1

Step-by-step explanation:

In many cases, the simplified expression is not undefined at the point of interest.

  $\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=\dfrac{\left(\dfrac{1-\sqrt{x}}{\sqrt{x}}\right)}{\sqrt{x}-1}=\dfrac{-1}{\sqrt{x}}$

This can be evaluated at x=1:

  -1/√1 = -1

Then, the limit is ...

  $\boxed{\lim\limits_{x\to 1}\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=-1}$

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A graph confirms this conclusion.