[tex](2x-5)^{ \frac{2x}{x-3} } = (2(x-3)+1)^{ \frac{2x - 6}{x-3} + \frac{6}{x-3} } = (2(x-3)+1)^{ \frac{2(x - 3)}{x-3} + \frac{6}{x-3} }[/tex]
Пусть b = x - 3
[tex](2(x-3)+1)^{ 2 + \frac{6}{x-3} } = (2b+1)^{ 2 + \frac{6}{b} }[/tex]
Применим второй замечательный предел
[tex](1 + 1/a)^{a} = e[/tex]
Пусть a = 1/(x - 3) = 1/b
[tex](1+ \frac{2}{a} )^{ 2 + 6a } = (1+ \frac{2}{a} )^{6a }*(1+ \frac{2}{a} )^{ 2} = ((1+ \frac{2}{a} )^{a })^{6}*(1+ \frac{2}{a} )^{ 2}[/tex]
[tex] = ((1+ \frac{2}{a} )^{ \frac{a}{2} })^{12}*(1+ \frac{2}{a} )^{ 2} = e^{12} * 1 = e^{12}[/tex]
