[latex] \lim_{n \to \infty} ((2x-1)/(2x+1))^{3x-1} [/latex]

[latex] \lim_{x \to \infty} ( \frac{2x-1}{2x+1})^{3x-1}==> \lim_{x \to \infty} (1+ \frac{2}{2x-1})^{1-3x} [/latex] [latex] \lim_{x \to \infty} ((1+ \frac{1}{ \frac{2x-1}{2} })^{ \frac{2x-1}{2}})^{ \frac{2-6x}{2x-1}}=>e^{ \lim_{x \to \infty} ( \frac{2-6x}{2x-1})}=>e^{-3} [/latex]