Question

решить второй замечательный предел

Answer 1

$lim_{x- \infty }(1 - \frac{2}{5x} ) ^{3x} \\ \\ lim_{x- \infty }(1 + \frac{1}{x} ) ^{x} = e \\ \\ lim_{x- \infty }(1 + ( - \frac{2}{5x} )) ^{ - \frac{5x}{2} \times( - \frac{6}{5} ) } = \\ = {e}^{ - \frac{6}{5} } = \frac{1}{ \sqrt[5]{ {e}^{6} } }$

Answer 2

\begin{gathered}lim_{x- > \infty }(1 - \frac{2}{5x} ) ^{3x} \\ \\ lim_{x- > \infty }(1 + \frac{1}{x} ) ^{x} = e \\ \\ lim_{x- > \infty }(1 + ( - \frac{2}{5x} )) ^{ - \frac{5x}{2} \times( - \frac{6}{5} ) } = \\ = {e}^{ - \frac{6}{5} } = \frac{1}{ \sqrt[5]{ {e}^{6} } } \end{gathered}

lim

x−>∞

(1−

5x

2

)

3x

lim

x−>∞

(1+

x

1

)

x

=e

lim

x−>∞

(1+(−

5x

2

))

−

2

5x

×(−

5

6

)

=

=e

−

5

6

=

5

e

6

1