求x趋于0的lim{1+1/2x^2-(1+x^2)^1/2}/{(cosx-e^(x^2))sin(x^2)
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求x趋于0的lim{1+1/2x^2-(1+x^2)^1/2}/{(cosx-e^(x^2))sin(x^2)
![求x趋于0的lim{1+1/2x^2-(1+x^2)^1/2}/{(cosx-e^(x^2))sin(x^2)](/uploads/image/z/374073-33-3.jpg?t=%E6%B1%82x%E8%B6%8B%E4%BA%8E0%E7%9A%84lim%7B1%2B1%2F2x%5E2-%EF%BC%881%2Bx%5E2%29%5E1%2F2%7D%2F%7B%28cosx-e%5E%28x%5E2%29%29sin%28x%5E2%29)
Taylor展式:原极限=lim{1+1/2x^2-(1+1/2x^2+(1/2)(-1/2)/2x^4+小o(x^4))}/{[1-x^2/2-(1+x^2)+小o(x^2)]x^2}=lim[1/8x^4+小o(x^4)]/[-3/2x^4+小o(x^4)]=-1/12.
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