高等数学,里面的一个分式如何判断它是趋向于无穷还是零? 如何判断一个函数在x取正无穷时的极限是0还是无穷?
\u9ad8\u7b49\u6570\u5b66\u4e2d\u51fd\u6570\u7684\u771f\u5206\u5f0f\u662f\u600e\u4e48\u5224\u65ad\u7684\uff1f\uff1f\u771f\u5206\u5f0f\u6307\u7684\u662f\u6709\u7406\u51fd\u6570\u4e2d\u7684\uff0c\u800c\u6709\u7406\u51fd\u6570\u6307\u7684\u662f\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u5546\uff0c\u5f53\u5206\u5b50\u7684\u591a\u9879\u5f0f\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u7684\u6b21\u6570\u65f6\uff0c\u6b64\u6709\u7406\u51fd\u6570\u79f0\u4e3a\u771f\u5206\u5f0f\u3002\u4e5f\u5c31\u662f\u901a\u8fc7\u5206\u5b50\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u6b21\u6570\u7684\u6bd4\u8f83\u5373\u53ef\u5224\u65ad\u3002
f(x) = lnx + x - x^2, x > 0
lim(lnx+x-x^2) = limx(lnx/x+1-x)
= lim(lnx/x+1-x)/(1/x)
\u5206\u5b50\u6781\u9650\u662f -\u221e\uff0c \u5206\u6bcd\u6781\u9650\u662f 0+\uff0c \u5206\u5f0f\u6781\u9650\u662f -\u221e \uff1b
\u53e6\u5916 lim(lnx+x-x^2) = -\u221e\u3002
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