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lim-x-0-1-x-1-x-c-x-c-2-




Question Number 52206 by SUJIT420 last updated on 04/Jan/19
lim_(x→0) (((1+x)^(1/x) −c)/x)=−(c/2)
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{1}/{x}} −{c}}{{x}}=−\frac{{c}}{\mathrm{2}} \\ $$
Commented by afachri last updated on 04/Jan/19
is it e ? or C Sir ??   i am thinking if that C, i find the eqn  diverges and get infinity for the limit. i  think it must be e.
$$\mathrm{is}\:\mathrm{it}\:{e}\:?\:\mathrm{or}\:\mathrm{C}\:\mathrm{Sir}\:??\: \\ $$$$\mathrm{i}\:\mathrm{am}\:\mathrm{thinking}\:\mathrm{if}\:\mathrm{that}\:\mathrm{C},\:\mathrm{i}\:\mathrm{find}\:\mathrm{the}\:\mathrm{eqn} \\ $$$$\mathrm{diverges}\:\mathrm{and}\:\mathrm{get}\:\mathrm{infinity}\:\mathrm{for}\:\mathrm{the}\:\mathrm{limit}.\:\mathrm{i} \\ $$$$\mathrm{think}\:\mathrm{it}\:\mathrm{must}\:\mathrm{be}\:{e}. \\ $$

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