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#