limits and derivatives concept

continuous function=連續性既function
discontinuous function=不連續性既function

而上圖的y=s(x)是不連續性既function, 因當x=3時,圖中出現圓形指y=s(x)呢條function既x係3時, 個答案係undefined...

舉一個例子,如 y=(x^2-9)/(x-3). 當x=3時, y=1/0=undefined... 是一個沒有解的function, 但當x<3 or x>3時,y是有解的... 証明當x=3是令這條function disconnect既點...

因此,可得以下結論...
(2^2-9)/(2-3)=5, (4^2-9)/(4-3)=7
if y=(x^2-9)/(x-3)

When x=3,
lim (x -> 3) (x^2-9)/(x-3)
=lim (x -> 3) (x+3)(x-3)/(x-3)
=lim (x -> 3) (x+3)
=6

即是當x愈接近3時, y愈接近6!!

|x|=絕對值
即是無論x是正數或是負數, 一但加了| |, 解必為正數

2014-06-08 16:43:15 補充：
是y=0/0=undefined才對

打錯,是discontinuous =﹏=

To Gethighandhigh：

你話圖入面哥個answer係continuous??