一道的高数题,设函数f(x)在x=0的某邻域二阶可导,且lim( sinx+f(x)x)/(x^3)=0求f(0).f'
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一道的高数题,
设函数f(x)在x=0的某邻域二阶可导,且lim( sinx+f(x)x)/(x^3)=0
求f(0).f'(0),f"(0)
我试着把fx设成o(x^2)-1还有用taylor公式换用,但行不通,
设函数f(x)在x=0的某邻域二阶可导,且lim( sinx+f(x)x)/(x^3)=0
求f(0).f'(0),f"(0)
我试着把fx设成o(x^2)-1还有用taylor公式换用,但行不通,
![一道的高数题,设函数f(x)在x=0的某邻域二阶可导,且lim( sinx+f(x)x)/(x^3)=0求f(0).f'](/uploads/image/z/6203329-25-9.jpg?t=%E4%B8%80%E9%81%93%E7%9A%84%E9%AB%98%E6%95%B0%E9%A2%98%2C%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8x%3D0%E7%9A%84%E6%9F%90%E9%82%BB%E5%9F%9F%E4%BA%8C%E9%98%B6%E5%8F%AF%E5%AF%BC%2C%E4%B8%94lim%28+sinx%2Bf%28x%29x%29%2F%28x%5E3%29%3D0%E6%B1%82f%280%29.f%27)
f(x)x=-sinx+o(x^3)=-x+x^3/6+o(x^3)
f(x)=-1+x^2/6+o(x^2);
所以f(0)=-1;f'(0)=0;f''(0)=(1/6)*2=1/3
f(x)=-1+x^2/6+o(x^2);
所以f(0)=-1;f'(0)=0;f''(0)=(1/6)*2=1/3
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