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[banana89]

\(\displaystyle{ \lim_{n\to\infty} ft( \frac{x^{2}+1}{2x^{2}-2} \right)^{x^{2}}}\)

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[wasap80]

\(\displaystyle{ \Leftrightarrow \lim_{ x\to } (\frac{2x^2-2 }{2x^2-2 } + \frac{-x^2+3}{2x^2-2 })^x^2= \lim_{x \to } (1+ \frac{-x^2+3}{2x^2-2 })^x^2 = \lim_{ x\to } (1+ \frac{1}{ \frac{2x^2-2 }{-x^2+3} } )^x^2= \lim_{ x\to } \frac{x^2}{ \frac{2x^2-2}{-x^2+3} } = \lim_{ x\to } \frac{-x^4+3x^2}{2x^2-2}= \lim_{x \to } \frac{-x^2+3}{2- \frac{2}{x^2} } = \lim_{ x\to } \frac{-x^2+3}{2}= ^{ \frac{-x^2+3}{2} }= ^{ -\infty }}\)

Zakładam, że ten znak\(\displaystyle{ \partial}\) to e