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Question Number 140071 by EDWIN88 last updated on 04/May/21

For what value of k is the following

continous function ?

f (x) = {\begin{cases} \frac{\sqrt{7 x + 2} - \sqrt{6 x + 4}}{x - 2}; if x ⩾ - \frac{2}{7} & x \neq 2 \\ k; if x = 2 \end{cases}

Answered by bobhans last updated on 04/May/21

\lim_{x \to 2} f (x) = \lim_{x \to 2} \frac{\sqrt{7 x + 2} - \sqrt{6 x + 4}}{x - 2}

= \lim_{x \to 2} \frac{(x - 2)}{(x - 2) (\sqrt{7 x + 2} + \sqrt{6 x + 4})}

= \lim_{x \to 2} \frac{1}{\sqrt{7 x + 2} + \sqrt{6 x + 4}} = \frac{1}{8} = k

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