Question

设F(x)在x=0处连续,已知当x趋近于0时,lim(1+f(x)/x)^1/sinx=e^2,求当x趋近于0时,lim

Answer 1

解

F(x)在x=0处连续

x→0,1/sinx~1/x

lim(1+f(x)/x)^1/sinx

=lim(1+f(x)/x)^1/x

=lim(1+f(x)/x)^x/f(x)*f(x)/x*1/x

=e^limf(x)/x^2

=e^2

所以limf(x)/x^2=2