limit and continuous function

1.a function f(x) is continuous at x =a if the following three conditions are satisfied.
1.f(a) exists.
2.lim x->a f(x) exists.
3.lim x->a fx) = f(a)In the other words,a continuous function satisfies the above 3 conditions.
(including condition 2)
Therefore,limit must exist if a function is continuous at x=a.
2.I haven't learnt differentiation yet so I can't help u..
3.yes
Acutally,the limit of a function f(x) as x approaches a exists and
lim x->a f(x) = L
IF AND ONLY IF
limx->a- f(x) = L(left hand limit) and lim x->a+ f(x) =L (right hand limit)
i.e. left hand limit = right hand limit = ordinary limit

Look at the graph below,

The function is discontinuous at x=a
But the left hand limit ( x approaches a from the left) and the right hand
limit (x approaches a from the right) are equal
So,lim x->a f(x) exists

圖片參考：http://imgcld.yimg.com/8/n/HA04937267/o/701204160006113873394570.jpg


2012-04-17 17:38:25 補充：
thx for ur information^^

2. Yes
f(x) is differentiable if lim[x->a] { f(x) - f(a)} / (x-a) exists
Consider lim[x->a] [f(x) - f(a)]
= lim[x->a] (x-a) * { f(x) - f(a)} / (x-a)
= 0,
lim[x->a] f(x) = lim[x->a] f(a) = f(a)
Thus it is continuous.