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

Lim ((1/(ex)))^(6x) =.....  x→0

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

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

Thanks Sir

$$\mathrm{Thanks}\:\mathrm{Sir} \\ $$

Commented by mathmax by abdo last updated on 21/Feb/20

you are welcome sir

$${you}\:{are}\:{welcome}\:{sir} \\ $$

Commented by zainal tanjung last updated on 23/Feb/20

Please help me....!!

$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}....!! \\ $$

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