Estatistica

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  • Publicado : 30 de março de 2013
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197 -

$lim_{h \to 0} \frac{(x + h)^3 - x^3}{h}$

$lim_{h \to 0} \frac{x^3 + 3x^2h ++3xh^2 +h^3 - x^3}{h}$

$lim_{h \to 0} \frac{3x^2 + 3hx +h^3}{h}$

$3x^2$\newline

205 -

$lim_{x \to 1} \frac{\sqrt{x}-1}{\sqrt[3]{x} - 1}$

$lim_{x \to 1} \frac{\sqrt{x}-1}{\sqrt[3]{x} - 1}*\frac{\sqrt{x}+1}{\sqrt[3]{x} +1}*\frac{\sqrt[3]{x^2} + \sqrt[3]{x} + 1}{\sqrt[3]{x^2} + \sqrt[3]{x} + 1}$

$lim_{x \to 1} \frac{(x+1)(\sqrt[3]{x^2} + \sqrt[3]{x} + 1)}{(x+1)(\sqrt{x} + 1)}$

$\frac{3}{2}$\newline

214 -

$lim_{x \to \infty} x(\sqrt{x^2+1} - x)$

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

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

$lim_{x \to \infty} \frac {1}{(\sqrt{x^2+1} + x)}$

$lim_{x \to \infty} \frac {1}{\sqrt{1+\frac{1}{x^2}}}$$\frac{1}{2}$
\newline

219 -

$\lim_{x \to 1} \frac{\sin x}{\sin(3\pi x)}$

$\pi x = y$

$\lim_{x \to \pi } \frac{\sin (y)}{\sin (3y)}$

$\lim_{x \to \pi }\frac{\sin (y)}{3\sin (y) \cos^2 (y) - \sin (2y)}$

$\lim_{x \to \pi } \frac{1}{3\cos^2 (y) - \sin^2 (y)}$

$\frac{1}{3}$
\newline

226 -

$\lim_{x \to \frac{\pi}{4}} \frac{\sin (x) - \cos (x)}{1- \tan(x)}$

$\lim_{x \to \frac{\pi}{4} } \frac{\sin (x) - \cos (x)}{\frac{\sin (x) - \cos (x)}{\cos(x)}}$

$\lim_{x \to \frac{\pi}{4} }-\cos(x)$

$-\frac{\sqrt{2}}{2}$
\newline

240 -

$\lim_{x \to 0} \frac{\sqrt{1+\sin(x)} - \sqrt{1-\sin(x)}}{x}$

$\lim_{x \to 0} \frac{\sqrt{1+\sin(x)} -\sqrt{1-\sin(x)}}{x}*\frac{\sqrt{1+\sin(x)} + \sqrt{1-\sin(x)}}{x}$

$\lim_{x \to 0} \frac{2\sin(x)}{(\sqrt{1+\sin(x)} + \sqrt{1-\sin(x)})x}$

$\frac{2}{2}$

$1$
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