求上下极限lim(x趋近0){∫(o-x) sintdt}/x

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  • 方法一:x趋近0,∫(0-x) sintdt趋近0,使用罗比达法则:lim(x趋近0){∫(0-x) sintdt}/x^2 =lim(x趋近0)d/dx∫(0-x) sintdt /2x =lim(x趋近0)sinx/2x 使用罗比达法则:=lim(x趋近0)cosx/2 =1/2.方法二:∫(0-x) sintdt =-cosx|0-x =1-cosx lim(x趋近0){∫(0-x) sintdt}/x^2 =lim(x趋近0)(1-cosx)/x^2 =lim(x趋近0)sinx/2x =lim(x趋近0)cosx/2 =1/2.