f(x)
=e^(-x^2) -1 ; x≤0
=ln(1+x) ; x>0
f(0-)=f(0) = e^(0) -1 = 0
f(0+)=lim(x->0) ln(1+x) =ln1 =0
x=0, f(x) 连续
f'(0-)
=lim(h->0) [e^(-h^2) -1 -f(0) ]/h
=lim(h->0) [e^(-h^2) -1 ) ]/h
=lim(h->0) -h^2/h
=lim(h->0) -h
=0
f'(0+)
=lim(h->0) [ln(1+h) -f(0) ]/h
=lim(h->0) ln(1+h)/h
=lim(h->0) h/h
=1
x=0, f(x)不可导
=e^(-x^2) -1 ; x≤0
=ln(1+x) ; x>0
f(0-)=f(0) = e^(0) -1 = 0
f(0+)=lim(x->0) ln(1+x) =ln1 =0
x=0, f(x) 连续
f'(0-)
=lim(h->0) [e^(-h^2) -1 -f(0) ]/h
=lim(h->0) [e^(-h^2) -1 ) ]/h
=lim(h->0) -h^2/h
=lim(h->0) -h
=0
f'(0+)
=lim(h->0) [ln(1+h) -f(0) ]/h
=lim(h->0) ln(1+h)/h
=lim(h->0) h/h
=1
x=0, f(x)不可导
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