exercicio resolvido

por **adauto martins** » Qua Abr 07, 2021 15:29

(ITA-1951)calcular

$\lim_{x\rightarrow\propto}logn/log(n-1)$

por **adauto martins** » Qua Abr 07, 2021 16:17

soluçao

faz-se

$y=log(n-1)\Rightarrow n=10^y+1$

logo

$logn/log(n-1)=log(10^y+1)/y=(1/y).log(10^y(1+(1/10^y) =log(10^y.(1+(1/10^y))^{1/y}=log({(10^y)}^{1/y}.(1+(1/10^y))^{1/y} =log10.({(1+(1/10^y)})^{1/y}=log10+log(1+(1/10^{y})^{1/y}$

entao

$\lim_{x\rightarrow\infty}logn/log(n-1)= \lim_{x\rightarrow\infty}(1+log(1+(1/10)^{1/y}= 1+log(\lim_{x\rightarrow\infty}(1+(1/10^y)^{1/y)}=1+log1=1$

exercicio resolvido

exercicio resolvido

exercicio resolvido

Re: exercicio resolvido

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