[tex]\displaystyle\bf\\2.a)\\3x=2x\cdot\frac{3}{2}\\\\\lim_{x \to \infty} \left(1+\frac{1}{2x}\right)^{3x}=\lim_{x \to \infty} \left(1+\frac{1}{2x}\right)^{2x\cdot\frac{3}{2} }=\\\\\\=\lim_{x \to \infty} \left(\left(1+\frac{1}{2x}\right)^{2x\right)^\frac{3}{2}}=\boxed{\bf e^\frac{3}{2}=e^{3/2}=e^{1,5}}\\\\\\2.b)\\tg(-1)\neq 0\implies\frac{0}{tg(-1)}=0\\\\\lim_{x\to0}\frac{x}{tg(x-1)}=\frac{0}{tg(0-1)}=\frac{0}{tg(-1)}=\boxed{\bf0}[/tex]
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[tex]\displaystyle\bf\\2.c)\\Limita~unei~fractii~de~polinoame~de~acelasi~grad~pentru~x\to\infty\\este~egala~cu~raportul~coeficientilor~lui~x~la~puterea~cea~mai~mare.\\\\\\\lim_{x\to\infty}\frac{x^2+x}{x^2-x}=\frac{1}{1}=\boxed{\bf1}[/tex]
