x无穷 [(1+x+1/x)^1/2 - (1+x)^1/2]x趋于派 [(cosx^2 + cosx^3)/sinx^3]
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![x无穷 [(1+x+1/x)^1/2 - (1+x)^1/2]x趋于派 [(cosx^2 + cosx^3)/sinx^3]](/uploads/image/z/15152321-65-1.jpg?t=x%E6%97%A0%E7%A9%B7+%5B%281%2Bx%2B1%2Fx%29%5E1%2F2+-+%281%2Bx%29%5E1%2F2%5Dx%E8%B6%8B%E4%BA%8E%E6%B4%BE+%5B%28cosx%5E2+%2B+cosx%5E3%29%2Fsinx%5E3%5D)
x无穷 [(1+x+1/x)^1/2 - (1+x)^1/2]x趋于派 [(cosx^2 + cosx^3)/sinx^3]
x无穷 [(1+x+1/x)^1/2 - (1+x)^1/2]
x趋于派 [(cosx^2 + cosx^3)/sinx^3]
x无穷 [(1+x+1/x)^1/2 - (1+x)^1/2]x趋于派 [(cosx^2 + cosx^3)/sinx^3]
分母有理化
[(1+x+1/x)^1/2 - (1+x)^1/2]
=[(1+x+1/x)^1/2-(1+x)^1/2][(1+x+1/x)^1/2+(1+x)^1/2]/[(1+x+1/x)^1/2+(1+x)^1/2]
=1/{x[(1+x+1/x)^1/2+(1+x)^1/2]}
则lim[(1+x+1/x)^1/2 - (1+x)^1/2]=0
[(cosx^2 + cosx^3)/sinx^3]
=(cosx)^2(1+cosx)/(sinx)^3
=(cosx)^2*2(cosx/2)^2/sinx^3
=2(cosx/2)^2/sinx^3
x趋于派,
可等同于:x趋于0
=2(sinx/2)^2/sinx^3
=2*x^2/4/sinx^3
=0