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数学
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y=x^2sin(1/x) ( x不等于0)当x=0的时候,y=0.怎么判断这个函数在0处可不可导,
人气:357 ℃ 时间:2019-08-19 05:50:10
解答
按定义做.
lim(x-->0)|(f(x)-f(0))/x - 0|
=lim(x-->0)|x^2sin(1/x)|/|x|
=lim(x-->0) |xsin(1/x)|
因为 |sin(1/x)|0) |xsin(1/x)| =0
即 y'(0)=0
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