设F(x)=∫(0趋向x) [(x-t)f(t)dt]/(sinx)^2 求lim(x趋向0)F(x),f(0)存在,

问题描述:

设F(x)=∫(0趋向x) [(x-t)f(t)dt]/(sinx)^2 求lim(x趋向0)F(x),f(0)存在,

本题少了个条件,f(x)连续lim(x趋向0)F(x)=lim(x趋向0)∫(0--->x) [(x-t)f(t)dt]/(sinx)²分母用等价无穷小代换=lim(x趋向0)∫(0--->x) [(x-t)f(t)dt]/x²分子拆开=lim(x趋向0) [x∫(0--->x) f(t)dt - ∫(0--...