※ 引述《wing10588 (tsubasa)》之铭言： : 是非题 : : 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. 错:不一定,若h(x)=f(x)+g(x)连续 不代表 f(x)+g(x)连续.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. 对:这是定理 : 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 其实题目有点不董,因为他说funtions on R 是说 此极限值等於R? 若是等於R,後者必成立,因为这是定理,而且还要会证 : 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 对:这是中间值定理 --

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