formulario limiti notevoli

$\underset{x\to 0}{\lim }\frac{ln(1+x)}{x}=1$

$\underset{x\to 0}{\lim }\frac{lo{g}_a(1+x)}{x}=\frac{1}{ln(a)}$

$\underset{x\to 0}{\lim }\frac{e^x-1}{x}=1$

$\underset{x\to 0}{\lim }\frac{a^x-1}{x}=ln(a)$

$\underset{x\to \pm \infty }{\lim }(1+\frac{1}{x}{)}^x=e$

$\underset{x\to 0}{\lim }\frac{(1+x{)}^c-1}{x}=c$

$\underset{x\to 0}{\lim }\frac{sin(x)}{x}=1$

$\underset{x\to 0}{\lim }\frac{1-cos(x)}{x^2}=\frac{1}{2}$

$\underset{x\to 0}{\lim }\frac{tg(x)}{x}=1$

$\underset{x\to 0}{\lim }\frac{arcsin(x)}{x}=1$

$\underset{x\to 0}{\lim }\frac{arctg(x)}{x}=1$

$\underset{x\to \pm \infty }{\lim }(1+\frac{a}{x}{)}^x=e^a$

$\underset{x\to 0}{\lim }(1+x{)}^{\frac{1}{x}}=e$

$\underset{x\to 0}{\lim }\frac{e^x-1}{tg(x)}=1$

$\underset{x\to 0}{\lim }\frac{ln(cos(x))}{x^2}=-\frac{1}{2}$

$\underset{x\to 0}{\lim }\frac{1-cos(x)}{x}=0$