Question

试确定a、b,使分段函数f(x)=ae^x+be^(-x),x ≥0;f(x)=1/x*ln(1+x),x＜0,在x=0

Answer 1

考察g(x)=ae^x+be^{-x},那么g(x)和f(x)在[0,+无穷)上相等,故有f'(0+)=g'(0+)=a-b.

同样,令h(x)=ln(1+x)/x可得f'(0-)=h'(0-)=-1.

然后你应该会做了.