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[Kajakov]

\(\displaystyle{ \lim_{n \to } ( \frac{4n-2}{4n+6} ) ^{3n}}\)

[blost]

\(\displaystyle{ \lim_{n \ } (\frac{n(4- \frac{2}{n}) }{n(4+ \frac{6}{n}) }) ^{3n}}\)
\(\displaystyle{ (\frac{4}{4}) ^{ } =1}\)

[lila]

\(\displaystyle{ \lim_{x\to\infty} ( \frac{4n-2}{4n+6} ) ^{3n} =}\)
\(\displaystyle{ \lim_{x\to\infty} ( \frac{4n+6-8}{4n+6} ) ^{3n} =}\)
\(\displaystyle{ \lim_{x\to\infty} ( 1 +\frac{1}{ \frac{4n+6}{-8} } ) ^{3n} =}\)
\(\displaystyle{ \lim_{x\to\infty} ( 1 +\frac{1}{ \frac{4n+6}{-8} } ) ^{( \frac{4n+6}{-8} ) ( \frac{-8}{4n+6} ) 3n} =}\)
\(\displaystyle{ \lim_{x\to\infty} e^{ \frac{-8 3n}{4n+6} =}\)
\(\displaystyle{ e ^{-6}}\)