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Question Number 26293 by d.monhbayr@gmail.com last updated on 23/Dec/17

lim_(x→∞) (3(√(1−x^3 +x)))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{3}\sqrt{\left.\mathrm{1}−{x}^{\mathrm{3}} +{x}\right)}\right. \\ $$

Answered by Joel578 last updated on 24/Dec/17

L = 3 .lim_(x→∞)  (√(1 + x − x^3 ))       = 3 . lim_(x→∞)   (√(x^3 ((1/x^3 ) + (1/x^2 ) − 1)))       = 3 . lim_(x→∞)   (√(∞^3 (−1)))       = i∞ (I didnt sure the answer is i∞ or just ∞)

$${L}\:=\:\mathrm{3}\:.\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{1}\:+\:{x}\:−\:{x}^{\mathrm{3}} } \\ $$$$\:\:\:\:\:=\:\mathrm{3}\:.\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\sqrt{{x}^{\mathrm{3}} \left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:−\:\mathrm{1}\right)} \\ $$$$\:\:\:\:\:=\:\mathrm{3}\:.\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\sqrt{\infty^{\mathrm{3}} \left(−\mathrm{1}\right)} \\ $$$$\:\:\:\:\:=\:{i}\infty\:\left(\mathrm{I}\:\mathrm{didnt}\:\mathrm{sure}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:{i}\infty\:\mathrm{or}\:\mathrm{just}\:\infty\right) \\ $$

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