Question

yudaaa recuerden que la respuesta no debe ser 0 y recuerden tomense su tiempo

Answer 1

Respuesta:

Explicación paso a paso:

1.

$\lim_{x \to \ 7} \frac{x^2-49}{x-7} \\\\ \lim_{x \to \ 7} \frac{(x-7)(x+7)}{x-7} \\\\ \lim_{x \to \ 7} (x+7)\\\\(7+7)=14$

2.

$\lim_{h \to \ 0} \frac{\sqrt{h+2}-\sqrt{2} }{h} \\\\ \lim_{h \to \ 0} \frac{(\sqrt{h+2}-\sqrt{2}) (\sqrt{h+2}+\sqrt{2}) }{h(\sqrt{h+2}+\sqrt{2})} \\\\\\ \lim_{h \to \ 0} \frac{(h+2)-2 }{h(\sqrt{h+2}+\sqrt{2})} \\\\ \lim_{h \to \ 0} \frac{h}{h(\sqrt{h+2}+\sqrt{2})} \\\\ \lim_{h \to \ 0} \frac{1}{(\sqrt{h+2}+\sqrt{2})} \\\\\frac{1}{\sqrt{0+2}+\sqrt{2} } =\frac{1}{2\sqrt{2} }$

3.

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