f(x)=e^(-1/x^2) ,求f'(0)f(x)={e^(-1/x^2) (x不=0时) 求f'(0)0 (x=0)

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f(x)=e^(-1/x^2),求f''(0)f(x)={e^(-1/x^2)(x不=0时)求f''(0)0(x=0)f(x)=e^(-1/x^2),求f''(0)f(x)={e^(-1/x^2)(x不=0

f(x)=e^(-1/x^2) ,求f'(0)f(x)={e^(-1/x^2) (x不=0时) 求f'(0)0 (x=0)
f(x)=e^(-1/x^2) ,求f'(0)
f(x)={e^(-1/x^2) (x不=0时) 求f'(0)
0 (x=0)

f(x)=e^(-1/x^2) ,求f'(0)f(x)={e^(-1/x^2) (x不=0时) 求f'(0)0 (x=0)
f(x)=e^(-1/x²) ,求f'(0)
f '(x)=[e^(-1/x²)](-1/x²)'=[e^(-1/x²)](2/x³)=(x⁻³)/[2e^(1/x²)]
x→0limf '(x)=x→0lim(-3x⁻⁴)/[2e^(1/x²)(-2/x³)]
=x→0lim(3x⁻¹)/[4e^(1/x²)]
=x→0lim(-3x⁻²)/[4e^(1/x²)(-2/x³)]
=x→0lim(3x)/[8e^(1/x²)]
=0
即f '(0)无定义,但极限存在,可重新定义f '(0)=x→0limf '(x)=0.