Re: [連續] 一些問題

[stillboy (joey)]

※ 引述《wing10588 (tsubasa)》之銘言：
: 是非題 :
: a.  If the function h(x)=f(x)+g(x) is continuous at the point  c
: ,then f(x) and g(x) are also continuous at c.

錯:不一定,若h(x)=f(x)+g(x)連續 不代表 f(x)+g(x)連續.例子可自己找
: b. If the function f(x) and g(x) are differentiable at the point  c then
: the function h(x)=f(x)+g(x) is differentiable at c.
對:這是定理
: c. Let f(x) and g(x) are functions on R ,then lim f(x)+lim g(x)=lim(f+g)(x)
:                                               x->c     x->c     x->c
其實題目有點不董,因為他說funtions on R 是說 此極限值等於R?
若是等於R,後者必成立,因為這是定理,而且還要會証
: d. If f(x) is a function on the closed internal [a,b] with f(a)<f(b),then
: for all L:f(a)<L<f(b)there exists c: a<=c <=b such that f(c)=L
對:這是中間值定理



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推 wing10588:謝謝~~~^^~~
推 stillboy:hi~之前沒看清楚,這是一個題組?
→ stillboy:第四題有盲點,因為他沒說f是連續
→ stillboy:所以第四題也是錯的
推 wing10588:是一組題的~