Lim-1-ex-6x-x-0-

Question Number 82425 by zainal tanjung last updated on 21/Feb/20

$$\mathrm{Lim}\:\left(\frac{\mathrm{1}}{\mathrm{ex}}\right)^{\mathrm{6x}} =….. \\ $$$$\mathrm{x}\rightarrow\mathrm{0} \\ $$

Commented by abdomathmax last updated on 21/Feb/20

let f(x)=((1/(ex)))^(6x) ⇒f(x)=e^(−6xln(ex)) =e^(−6x{1+lnx)) =e^(−6x−6xlnx) →1 (x→o)

$${let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}}{{ex}}\right)^{\mathrm{6}{x}} \:\Rightarrow{f}\left({x}\right)={e}^{−\mathrm{6}{xln}\left({ex}\right)} \\ $$$$={e}^{−\mathrm{6}{x}\left\{\mathrm{1}+{lnx}\right)} \:={e}^{−\mathrm{6}{x}−\mathrm{6}{xlnx}} \rightarrow\mathrm{1}\:\left({x}\rightarrow{o}\right) \\ $$

Commented by zainal tanjung last updated on 21/Feb/20