Question

36.17. Найдите предел:
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Answer 1

$3) \lim_{x \to\ 16} \frac{4-\sqrt{x} }{x-16} = \frac{0}{0} -$ неопределённость

$\lim_{x \to \ 16} \frac{-(\sqrt{x}-4)}{(\sqrt{x} -4)(\sqrt{x} +4)} = \lim_{x \to \ 16} \frac{-1}{\sqrt{x} +4} = \frac{-1}{4+4} = \frac{-1}{8}$

$6) \lim_{x \to \ 2}\frac{x^2-4}{\sqrt{2x-3}-1 } = \frac{0}{0} -$ неопределённость

$\lim_{x \to \ 2} \frac{(x^2-4)(\sqrt{2x-3}+1) }{(\sqrt{2x-3}-1)(\sqrt{2x-3}+1) } = \lim_{x \to \ 2} \frac{(x^2-4)(\sqrt{2x-3}+1)}{2x-3-1}= \lim_{x \to \ 2} \frac{(x-2)(x+2)(\sqrt{2x-3}+1)}{2(x-2)} = \lim_{x \to \ 2} \frac{(x+2)(\sqrt{2x-3}+1)}{2} = \frac{(2+2)(\sqrt{2x-3}+1) }{2} = 4$