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Find \( \lim _{x \rightarrow \infty} x\left(2 x+\left(\sqrt[3]{x^{3}+x^{2}+1}+\sqrt[3]{x^{3}-x^{2}+1}\right)\right) \) (a) 219 (b) \( 7 / 9 \) (c) \( 1 / 9 \) (d) None of these |
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Answer» \(\lim\limits_{x\to \infty}\) x(2x + (x3 + x2 + 1)1/3 + (x3 - x2 + 1)1/3) = \(\lim\limits_{x\to \infty}\) x2(2 + (1 + 1/x + 1/x3)1/3 + (1 - 1/x + 1/x2)1/3) = \(\infty^2\)(2 + 1 + 1) \((\because 1/\infty=0)\) = \(\infty\) = not defined |
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