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03-可导连续可微之间关系

03-可导连续可微之间关系

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什么是导数 ^s3PN95ss

· 指函数在某一点处变化的快慢,是一种变化率 · 定义: ^mnISkyhG

什么是微分 ^q7dyuwFN

· 是指函数在某一点处(趋近于无穷小)的变化量,是一种变化的量 · 定义: ^QNZwxv6Q

什么是连续 ^TZdG2jLA

· 从图像上看就是函数图像不间断,严格的数学语言就是: 在一点上的极限值就等于它的函数值 · 定义: ^tGoe9or0

可导一定连续 ^74r8BRM7

因为根据导数定义: 当x和x0大小趋向于一致时,分母极限为0,如果导数极限想要存在, 则分子极限也需要为0.所以有这一点的Lim有f(x)=f(x0),即 表示这一点连续; ^A5spL71E

若曲线光滑渐变 (可导) , 其必然没有断开 (连续) 但曲线没有断开 (连续) , 其不一定是光滑渐变的 (例如光进入另一介质的那种偏折) ^Se0Zmia6

连续不一定可导 ^ad0BOvO3

可导 ^sUy5tq0c

可微 ^SqqIq4WX

· dy = k * dx , 若有dy,就称可微 ^hHiRDBZR

因为微分当中:dy = k * dx 如果可导,则dy/dx = k 所以可导一定可微分 ^1mRESnLo

可导一定可微 ^G7Kn8JHG

因为微分当中:dy = k * dx 当微分存在时,dy存在,因此 · dy/dx = k 当中的k存在 所以可微一定可导 ^WgMPrtYn

可微一定可导 ^3gaDIqr2

因为微分当中:dy = k * dx 当微分存在时,dy存在,因此:dy/dx = k 中k存在 连续当中,如果dx趋向于0时,dy趋向于0,则表示连续 因为dy = k * dx中dx为无穷小,k为确定值,所以dy趋向于0 即可微一定可导 ^ouPmPVKY

可微一定连续 ^rLdHpBRg

连续存在时:dx趋向于0,dy趋向于0 即dy = 0,若dy值等0,就称连续 但 ^CotkhqOy

连续不一定可微 ^PGDiPh7g

不能推出它们的比值为K ^5lUeCLi3

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