limx→0 ∫[0,x^1/2](1-cost2)dt/x5/2
问题描述：
limx→0 ∫[0,x^1/2](1-cost2)dt/x5/2
limx→0 ∫[0,x^1/2](1-cost²)dt/x5/2,急求解答
limx→0 ∫[0,x^1/2](1-cost²)dt/x^5/2
答
罗比达法则可得.原式=(1-cosx)/2x^(1/2)*2/(5*(x)^(3/2))=(1-cosx)/5x^2.又由等价无穷小代换可得.原式=1/2*x^2/5x^2=1/10