设函数f(x)=x的k次方sin1/x,x≠0,0,x=0 (1)当k取何值时,f(x)在点x=0上处可导(2)当k取何值时,f’(x)在点x=0处连续

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设函数f(x)=x的k次方sin1/x,x≠0,0,x=0(1)当k取何值时,f(x)在点x=0上处可导(2)当k取何值时,f’(x)在点x=0处连续设函数f(x)=x的k次方sin1/x,x≠0,0

设函数f(x)=x的k次方sin1/x,x≠0,0,x=0 (1)当k取何值时,f(x)在点x=0上处可导(2)当k取何值时,f’(x)在点x=0处连续
设函数f(x)=x的k次方sin1/x,x≠0,0,x=0 (1)当k取何值时,f(x)在点x=0上处可导(2)当k取何值时,f’(x)在点x=0处连续

设函数f(x)=x的k次方sin1/x,x≠0,0,x=0 (1)当k取何值时,f(x)在点x=0上处可导(2)当k取何值时,f’(x)在点x=0处连续
(2)当 k>0 时,lim{|(x^k)*sin(1/x)|}≤lim{|x^k|}=0=f(0),函数在 x=0 处连续;
(1)当 k>1 时,f'(x)=lim{[f(x)-f(0)]/(x-0)}=lim{[(x^k)*sin(1/x)]/x}=lim{[x^(k-1)]*sin(1/x)}=0;