[tex]\lim_{x \to \infty} \frac{2x+1}{2x-1}^{\frac{2*x^{2} +x+4}{x-4} }[/tex] Решите пожалуйста лимит. Created by lepme. algebra-ru

tex] Решите пожалуйста лимит...

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[tex]\lim_{x \to \infty} \frac{2x+1}{2x-1}^{\frac{2*x^{2} +x+4}{x-4} }[/tex]
Решите пожалуйста лимит

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$\lim\limits _{x \to \infty}\Big (\frac{2x+1}{2x-1}\Big )^{\frac{2x^2+x+4}{x-4}}=\lim\limits _{x \to \infty}\Big (\Big (1+\frac{2}{2x-1}\Big )^{\frac{2x-1}{2}}\Big )^{\frac{2}{2x-1}\cdot \frac{2x^2+x+4}{x-4}}=\\\\\\=e^{\lim\limits _{x \to \infty}\frac{4x^2+2x+8x}{2x^2-9x+4}}=e^{\frac{4}{2}}=e^2$

$P.S.\; \; \; \lim\limits _{x \to \infty}\frac{4x^2+2x+8}{2x^2-9x+4}=\lim\limits _{x \to \infty}\frac{4+\frac{2}{x}+\frac{8}{x^2}}{2-\frac{9}{x}+\frac{4}{x^2}} =\frac{4}{2}=2$

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