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lim-x-3-2-6-2x-6-2x-36-4x-2-




Question Number 195013 by horsebrand11 last updated on 22/Jul/23
      lim_(x→3)  (((2((√6)−(√(2x)) +(√(6−2x))))/( (√(36−4x^2 )))) )
$$\:\:\:\:\:\:\underset{\mathrm{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}\left(\sqrt{\mathrm{6}}−\sqrt{\mathrm{2x}}\:+\sqrt{\mathrm{6}−\mathrm{2x}}\right)}{\:\sqrt{\mathrm{36}−\mathrm{4x}^{\mathrm{2}} }}\:\right) \\ $$
Answered by cortano12 last updated on 22/Jul/23
    = lim_(x→3)  ((2(((√(6−2x))/( (√6) +(√(2x)))) +1 ))/( (√(6+2x))))       =   determinant ((((2/( (√(12)))) = (1/3)(√3))))
$$\:\:\:\:=\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{2}\left(\frac{\sqrt{\mathrm{6}−\mathrm{2}{x}}}{\:\sqrt{\mathrm{6}}\:+\sqrt{\mathrm{2}{x}}}\:+\mathrm{1}\:\right)}{\:\sqrt{\mathrm{6}+\mathrm{2}{x}}} \\ $$$$\:\:\:\:\:=\:\:\begin{array}{|c|}{\frac{\mathrm{2}}{\:\sqrt{\mathrm{12}}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\sqrt{\mathrm{3}}}\\\hline\end{array} \\ $$

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