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lim x infty (1+ 1/x)^3x |
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Answer» \(\lim\limits_{\mathrm x\to \infty}\)\(\left(1+\frac{1}{\mathrm x}\right)^{3\mathrm x}\) [1∞type] = Exp\(\left\{\lim\limits_{\mathrm x\to \infty}\frac{1}{\mathrm x}\times 3\mathrm x\right\}\) \(\Big(\because \) If \(\lim\limits_{\mathrm x \to \infty}\)\(\left(f(\mathrm x)\right)^{g(\mathrm x)}\) = [1∞type] then \(\lim\limits_{\mathrm x \to \infty}\) \(\left(f(\mathrm x)\right)^{g(\mathrm x)}\) = Exp\(\left\{\lim\limits_{\mathrm x \to \infty}(f(\mathrm x)-1){g(\mathrm x)}\right\}\Big)\) = Exp\(\left\{\lim\limits_{\mathrm x \to \infty}3\right\}\) \(= e^3\) |
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