若limg(x)=0,且在x0的某去心领域内g(x)不等于0.lim[f(x)/g(x)]=A则limf(x)必等于0,
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若limg(x)=0,且在x0的某去心领域内g(x)不等于0.lim[f(x)/g(x)]=A则limf(x)必等于0,为什么?所有都是x趋向于x0
![若limg(x)=0,且在x0的某去心领域内g(x)不等于0.lim[f(x)/g(x)]=A则limf(x)必等于0,](/uploads/image/z/15933153-57-3.jpg?t=%E8%8B%A5limg%28x%29%3D0%2C%E4%B8%94%E5%9C%A8x0%E7%9A%84%E6%9F%90%E5%8E%BB%E5%BF%83%E9%A2%86%E5%9F%9F%E5%86%85g%EF%BC%88x%EF%BC%89%E4%B8%8D%E7%AD%89%E4%BA%8E0.lim%5Bf%28x%29%2Fg%28x%29%5D%3DA%E5%88%99limf%EF%BC%88x%EF%BC%89%E5%BF%85%E7%AD%89%E4%BA%8E0%2C)
很简单的问题:
limg(x)=0说明当自变量x趋向于x0,g(x)是无穷小量,即得1/g(x)是无穷大量;
若limf(x)不等于0,则lim[f(x)/g(x)]必为无穷大量,而不会等于常数A,所以limf(x)必等于0.
limg(x)=0说明当自变量x趋向于x0,g(x)是无穷小量,即得1/g(x)是无穷大量;
若limf(x)不等于0,则lim[f(x)/g(x)]必为无穷大量,而不会等于常数A,所以limf(x)必等于0.
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