\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
(1+
x
1
=e
(1+(−
))
−
×(−
5
6
=
e
\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