What is the limit $limxtoa (a-x)/(sqrta-sqrtx)$ ?

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$limxtoa (a-x)/(sqrta-sqrtx)$

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Answer 1 · 2018-03-28T00:24:58

$2sqrta$

We have, for $x ne a$

$(a-x)/(sqrta -sqrtx) = ((sqrta)^2-(sqrtx)^2)/(sqrta -sqrtx) = ((sqrta-sqrtx)(sqrta+sqrtx))/(sqrta -sqrtx) = sqrta+sqrtx$

Thus:

$lim_{x to a} (a-x)/(sqrta -sqrtx) = lim_(x to a) (sqrta+sqrtx) = 2sqrta$