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




Question Number 6689 by Tawakalitu. last updated on 13/Jul/16
limit           1 + (1/(1 − x))  x ⇢ ∞
$${limit}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}} \\ $$$${x}\:\dashrightarrow\:\infty \\ $$
Answered by FilupSmith last updated on 14/Jul/16
lim_(x→∞)  1+(1/(1−x)) = 1+(1/(1−∞))  =1−(1/∞)  =1−0  =1
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}−{x}}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}−\infty} \\ $$$$=\mathrm{1}−\frac{\mathrm{1}}{\infty} \\ $$$$=\mathrm{1}−\mathrm{0} \\ $$$$=\mathrm{1} \\ $$
Commented by Tawakalitu. last updated on 14/Jul/16
Thanks
$${Thanks} \\ $$

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