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limit-1-1-x-1-x-




Question Number 6692 by Tawakalitu. last updated on 14/Jul/16
limit        1 + (1/(x − 1))  x → ∞
$${limit}\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}\:−\:\mathrm{1}} \\ $$$${x}\:\rightarrow\:\infty \\ $$
Answered by FilupSmith last updated on 14/Jul/16
lim_(x→∞)  1+(1/(x−1))=1+(1/(∞−1))  =1+(1/∞)  =1+0  =1
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{1}+\frac{\mathrm{1}}{{x}−\mathrm{1}}=\mathrm{1}+\frac{\mathrm{1}}{\infty−\mathrm{1}} \\ $$$$=\mathrm{1}+\frac{\mathrm{1}}{\infty} \\ $$$$=\mathrm{1}+\mathrm{0} \\ $$$$=\mathrm{1} \\ $$

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