lim(x→+∞)[∫(上限为x,下限为0)(arctan t)^2dt]/[(x^2)+1 ]^(1/2)
问题描述:
lim(x→+∞)[∫(上限为x,下限为0)(arctan t)^2dt]/[(x^2)+1 ]^(1/2)
答
lim∫(arctant)²dt/√(x²+1)用洛必达法则=lim(arctanx)²/{[1/2(x²+1)^(-1/2)](2x)}=lim(arctanx)²√(x²+1)/x=lim(arctanx)²·lim√(x²+1)/x=π²/4=lim