求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
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求lim[1+(sin1/x+cos1/x-1)]^x(x趋于无穷大)求lim[1+(sin1/x+cos1/x-1)]^x(x趋于无穷大)求lim[1+(sin1/x+cos1/x-1)]^x(x趋
求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
令t=1/x,t趋于0
lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
=lim(sint+cost)^(1/t)
=lim[1+(sint+cost-1)]^{[1/(sint+cost-1)]*(sint+cost-1)/t}
=e(因t趋于0时,lim(sint+cost-1)/t=lim(cost-sint)=1)
求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
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