常见公式

皆为做题积累

1.极限

1.1 \(\lim_{x->0^+} x^\alpha *lnx\) = 0 (\(\alpha\) > 0)

• 推导
  • = \(\lim_{x->0^+} \frac {lnx}{x^{-\alpha}}\) 洛必达
  • = \(\lim_{x->0^+} \frac {\frac {1}{x}} {-\alpha* x^{-\alpha-1} }\)
  • = \(\lim_{x->0^+} \frac {1} {-\alpha* x^{-\alpha} }\)
  • = \(\lim_{x->0^+} \frac {* x^{\alpha}} {-\alpha }\)
  • = 0

导数

ln(x + \(\sqrt {1+x^2}\)) = \(\frac {1}{\sqrt {1+ x^2}}\)

积分