Question

求大神帮忙,求同一函数的左右极限!

Answer 1

lim(x→0+)1/x=+∞,lim(x→0+)e^(1/x)=+∞,lim(x→0+)f(x)=lim(x→0+){[1/e^(1/x)]-1}/{[1/e^(1/x)]+1}=-1

lim(x→0-)1/x=-∞,lim(x→0-)e^(1/x)=0,lim(x→0-)f(x)=lim(x→0-)[1-e^(1/x)]/[1+e^(1/x)]=1

lim(x→0+)f(x)≠lim(x→0-)f(x)

∴lim(x→0)f(x)不存在