作业帮lim→0{1/(xsinx)[∫(上限x^2,下限0)(1+3t)^(1/t) dt
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lim→0{1/(xsinx)[∫(上限x^2,下限0)(1+3t)^(1/t) dt
lim→0{1/(xsinx)[∫(上限x^2,下限0)(1+3t)^(1/t) dt
lim→0{1/(xsinx)[∫(上限x^2,下限0)(1+3t)^(1/t) dt
上下用洛必达法则求导得
lim(x->0)[2x(1+3x^2)^(1/x^2)]/(xcosx+sinx)
=lim(x->0)2xe^3/(xcosx+sinx)
=lim(x->0)2e^3/(cosx-xsinx+cosx)
=2e^3/(1-0+1)=e^3
lim→0{1/(xsinx)[∫(上限x^2,下限0)(1+3t)^(1/t) dt
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