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As expected, if you plug in 0 into the initial equation, the answer is undefined or indeterminate. I tried multiplying the conjugate $\frac1{\sqrt{x+h-2}}+\frac1{\sqrt{x-2}}$ to the numerator and the denominator, but i couldn't simplify this equation enough to avoid the indeterminate value.

$$\lim_{h\to 0} \dfrac{\frac1{\sqrt{x+h-2}}-\frac1{\sqrt{x-2}}}{h}$$

  • 2
    You know that $\frac a b - \frac c d = \frac{ad - bc}{bd}$, right?2011-09-13
  • 0
    If you know differentiation, you can "cheat": Can you see that this is the derivative of $f(x)=1/\sqrt{x-2}$ at $x$?2011-09-13

2 Answers 2