高数极限正负趋向Lim(x→0−)f(x)=(e1/x-1)/(e1/x+1)=_1Lim(x→0+)f(x)=(e1/x-1)/(e1/x+1)=+1请问为什么x正趋向于0,f(x)就等于正1;x负趋向于0,f(x)就等于-1?正负趋向有什么规则可循呢?(式中括号里为
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![高数极限正负趋向Lim(x→0−)f(x)=(e1/x-1)/(e1/x+1)=_1Lim(x→0+)f(x)=(e1/x-1)/(e1/x+1)=+1请问为什么x正趋向于0,f(x)就等于正1;x负趋向于0,f(x)就等于-1?正负趋向有什么规则可循呢?(式中括号里为](/uploads/image/z/8696991-39-1.jpg?t=%E9%AB%98%E6%95%B0%E6%9E%81%E9%99%90%E6%AD%A3%E8%B4%9F%E8%B6%8B%E5%90%91Lim%28x%E2%86%920%26%238722%3B%29f%28x%29%3D%28e1%2Fx-1%29%2F%28e1%2Fx%2B1%29%3D_1Lim%28x%E2%86%920%2B%29f%28x%29%3D%28e1%2Fx-1%29%2F%28e1%2Fx%2B1%29%3D%2B1%E8%AF%B7%E9%97%AE%E4%B8%BA%E4%BB%80%E4%B9%88x%E6%AD%A3%E8%B6%8B%E5%90%91%E4%BA%8E0%2Cf%EF%BC%88x%EF%BC%89%E5%B0%B1%E7%AD%89%E4%BA%8E%E6%AD%A31%EF%BC%9Bx%E8%B4%9F%E8%B6%8B%E5%90%91%E4%BA%8E0%2Cf%EF%BC%88x%EF%BC%89%E5%B0%B1%E7%AD%89%E4%BA%8E-1%3F%E6%AD%A3%E8%B4%9F%E8%B6%8B%E5%90%91%E6%9C%89%E4%BB%80%E4%B9%88%E8%A7%84%E5%88%99%E5%8F%AF%E5%BE%AA%E5%91%A2%3F%EF%BC%88%E5%BC%8F%E4%B8%AD%E6%8B%AC%E5%8F%B7%E9%87%8C%E4%B8%BA)
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高数极限正负趋向Lim(x→0−)f(x)=(e1/x-1)/(e1/x+1)=_1Lim(x→0+)f(x)=(e1/x-1)/(e1/x+1)=+1请问为什么x正趋向于0,f(x)就等于正1;x负趋向于0,f(x)就等于-1?正负趋向有什么规则可循呢?(式中括号里为
高数极限正负趋向
Lim(x→0−)f(x)=(e1/x-1)/(e1/x+1)=_1
Lim(x→0+)f(x)=(e1/x-1)/(e1/x+1)=+1
请问为什么x正趋向于0,f(x)就等于正1;x负趋向于0,f(x)就等于-1?正负趋向有什么规则可循呢?(式中括号里为:e的x分之一,整体再加/减1,“/”为除法号)
高数极限正负趋向Lim(x→0−)f(x)=(e1/x-1)/(e1/x+1)=_1Lim(x→0+)f(x)=(e1/x-1)/(e1/x+1)=+1请问为什么x正趋向于0,f(x)就等于正1;x负趋向于0,f(x)就等于-1?正负趋向有什么规则可循呢?(式中括号里为
x正趋向于0时,1/x趋于正无穷,所以e^1/x趋于正无穷
所以
Lim(x→0+)(e^(1/x)-1)/(e^(1/x)+1)=1
x负趋向于0时,1/x趋于负无穷,所以e^1/x趋于0
所以
Lim(x→0-)(e^(1/x)-1)/(e^(1/x)+1)=-1/1=-1
正负趋向都是趋于某个值,只是比趋于的那个值大还是小的区别
如果还不懂的话,再补充吧……