Limites Notáveis

limx→+∞axxp=+∞${\displaystyle \underset{x\to +\infty }{lim}\frac{a^x}{x^p}=+\infty }$      (a,p∈R)${\displaystyle (a,p\in ℝ)}$	limx→+∞logaxx=0${\displaystyle \underset{x\to +\infty }{lim}\frac{{\log }_{a}x}{x}=0}$      (a>1,a∈R)${\displaystyle (a>1,a\in ℝ)}$
limx→0ex−1x=1${\displaystyle \underset{x\to 0}{lim}\frac{e^x-1}{x}=1}$	limx→0ln(x+1)x=1${\displaystyle \underset{x\to 0}{lim}\frac{\ln (x+1)}{x}=1}$
limx→0sinxx=1${\displaystyle \underset{x\to 0}{lim}\frac{\sin x}{x}=1}$	limx→+∞sinxx=0${\displaystyle \underset{x\to +\infty }{lim}\frac{\sin x}{x}=0}$
limun→+∞(1+kun)un=ek${\displaystyle \underset{u_n\to +\infty }{lim}{(1+\frac{k}{u_n})}^{u_n}=e^k}$	lim(1+1n)n=e${\displaystyle lim{(1+\frac{1}{n})}^n=e}$      (n∈N)${\displaystyle (n\in \mathbb{N})}$