当x→0时,1-cos2x与∫(0→sinx)ln(1+at)dt为等价无穷小,则a=?
问题描述:
当x→0时,1-cos2x与∫(0→sinx)ln(1+at)dt为等价无穷小,则a=?
答
lim(x→0)1-cos2x/∫(0→sinx)ln(1+at)dt
=lim(x→0)2x²/∫(0→sinx)ln(1+at)dt
=lim(x→0)4x/ln(1+asinx)*cosx
=lim(x→0)4x/asinx
=4/a
=1
所以
a=4