Saturday 30 April 2016

calculus - Finding limit of $limlimits_{hto 0} frac1{h}left(frac1{sqrt{x+h-2}}-frac1{sqrt{x-2}}right)$

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.




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

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