设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )A.\x05仅当lim(x--0)f(x)=lim(x--0) x^n•sin(1/x)=f(0)=0时,才可微B.\x05在任何条件都可微C.\x05当且仅当
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![设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )A.\x05仅当lim(x--0)f(x)=lim(x--0) x^n•sin(1/x)=f(0)=0时,才可微B.\x05在任何条件都可微C.\x05当且仅当](/uploads/image/z/15242576-32-6.jpg?t=%E8%AE%BEf%28x%29%3Dx%5En%26%238226%3Bsin%281%2Fx%29+%28x%E2%89%A00%29%2C%E4%B8%94f%280%29%3D0%2C%E5%88%99f%28x%29%E5%9C%A8x%3D0%E5%A4%84%28+%29%E8%AE%BEf%28x%29%3Dx%5En%26%238226%3Bsin%281%2Fx%29+%28x%E2%89%A00%29%2C%E4%B8%94f%280%29%3D0%2C%E5%88%99f%28x%29%E5%9C%A8x%3D0%E5%A4%84%28+%29A.%5Cx05%E4%BB%85%E5%BD%93lim%28x--0%29f%28x%29%3Dlim%28x--0%29+x%5En%26%238226%3Bsin%281%2Fx%29%3Df%280%29%3D0%E6%97%B6%2C%E6%89%8D%E5%8F%AF%E5%BE%AEB.%5Cx05%E5%9C%A8%E4%BB%BB%E4%BD%95%E6%9D%A1%E4%BB%B6%E9%83%BD%E5%8F%AF%E5%BE%AEC.%5Cx05%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93)
设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )A.\x05仅当lim(x--0)f(x)=lim(x--0) x^n•sin(1/x)=f(0)=0时,才可微B.\x05在任何条件都可微C.\x05当且仅当
设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )
设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )
A.\x05仅当lim(x--0)f(x)=lim(x--0) x^n•sin(1/x)=f(0)=0时,才可微
B.\x05在任何条件都可微
C.\x05当且仅当n>1时才可微
D.\x05因sin(1/x)在x=0处无定义,所以不可微
设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )设f(x)=x^n•sin(1/x) (x≠0),且f(0)=0,则f(x)在x=0处( )A.\x05仅当lim(x--0)f(x)=lim(x--0) x^n•sin(1/x)=f(0)=0时,才可微B.\x05在任何条件都可微C.\x05当且仅当
n>1时有
f'(0)=lim (f(x)-f(0))/x = lim x^(n-1)sin(1/x) =0 (无穷小乘有界量)
n