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

Posted by haifeng on 2019-10-27 11:02:43 last update 2019-10-27 11:03:22 | Edit | Answers (1)

求

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

Posted by haifeng on 2019-10-27 11:06:42

$lim_{x \to \infty} (\frac{x^{2} + x + 1}{x^{2} + x})^{2 x^{2}} = lim_{x \to \infty} [(1 + \frac{1}{x^{2} + x})^{x^{2} + x}]^{\frac{2 x^{2}}{x^{2} + x}} = e^{2} .$

问题及解答

求 limx→∞(x2+x+1x2+x)2x2.

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