Question

x趋于0+与x趋于0-分别怎么求极限啊？

Answer 1

x→0+，即x = 0 + ε，x = ε
x→0-，即x + ε = 0，x = - ε
ε是一个趋向0的数值
例如求lim(x→0) e^(1/x)
当x→0+时，令x = ε
即lim(x→0+) e^(1/x) = lim(ε→0) e^(1/ε) = e^∞ = +∞
当x→0-时，令x = - ε
即lim(x→0-) e^(1/x) = lim(ε→0) e^(1/(- ε)) = lim(ε→0) e^(- 1/ε)
= lim(ε→0) 1/e^(1/ε) = 1/e^∞ = 0