lim(x-∞)(e^x+cosx)/(e^x-sinx)=本人比较愚钝,
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lim(x-∞)(e^x+cosx)/(e^x-sinx)=本人比较愚钝,
lim(x-∞)(e^x+cosx)/(e^x-sinx)=
本人比较愚钝,
lim(x-∞)(e^x+cosx)/(e^x-sinx)=本人比较愚钝,
两种思路:
1.由于正弦函数和余弦函数都是有界函数,所以sinx和cosx都是有界量,可以无视掉,所以就变成了上下全是e^x,所以这个极限值应该是1.
2.如果上面那个你听着不容易理解,你可以这样想,分子分母同时除以e^x,极限就变成了(1+cosx/e^x)/(1-sinx/e^x),由于正余弦函数都有界,所以cosx/e^x和sinx/e^x的极限值都等于0,所以原极限=1/1=1.
lim(e^x)cosx= x→+∞
lim(x-∞)(e^x+cosx)/(e^x-sinx)=本人比较愚钝,
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