求上下极限lim(x趋近0)∫(o-x){根号下(1+x^2)dt}/x
问题描述:
求上下极限lim(x趋近0)∫(o-x){根号下(1+x^2)dt}/x
求上下极限lim(x趋近0){∫(o-x)根号下(1+x^2)d}/x 应该是这样
答
x趋近0,∫(0-x){根号下(1+t^2)dt}趋近0,使用罗比达法则:lim(x趋近0)∫(0-x){根号下(1+t^2)dt}/x =lim(x趋近0)d/dx∫(0-x){根号下(1+t^2)dt} =lim(x趋近0)根号下(1+x^2) =1.