[tex]\displaystyle \lim_{x \to\pm \infty} \frac{1}{x} =0\\
\lim_{x \to 0, x\ \textgreater \ 0\ sau\ x\ \textless \ 0} \frac{1}{x} =\pm\infty\\\\
\lim_{x \to\pm \infty} (1+ \frac{1}{x} )^x=e\\
\lim_{x \to\infty} (1+ x)^{\frac{1}{x}}=e\\
\lim_{x \to\pm \infty} (1+ \frac{1}{x} )^x=e\\
\lim_{x \to\pm \infty } \frac{3x^2+4x+5}{4x^2+4} =\frac{3}{4}\\
\lim_{x \to\pm \infty } \frac{3x^2+4x+5}{4x^3+4} =0\\
\lim_{x \to\pm \infty } \frac{3x^3+4x+5}{4x^2+4} =\pm \infty \\[/tex]
[tex]\displaystyle \lim_{x \to0,x\ \textgreater \ 0 } lnx=-\infty\\
\lim_{x \to+\infty } \sqrt{x+1}- \sqrt{x} =0[/tex]
[tex] \displaystyle \lim_{x \to+ \infty} \frac{1}{lnx} =0[/tex]
[tex]constanta'=0\\
x'=1\\
(x^{n})'=nx^{n-1}\\
(e^x)'=e^x\\
(a^x)'=a^x\cdot lna\\
( \sqrt{x} )'= \frac{1}{2 \sqrt{x} } \\
(lnx)'= \frac{1}{x} \\
(sinx)'=cosx\\
(cosx)'=-sinx\\
(arctgx)'= \frac{1}{x^2+1} \\[/tex]
