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Reviewed CSCA STEM Chinese question · Standard

在高等数学中,若函数f(x)在区间[a,b]上连续,且f(a)与f(b)异号,则根据零点定理,在区间(a,b)内至少存在一点ξ,使得f(ξ)_。

  1. 大于零
  2. 小于零
  3. 等于零
  4. 不存在
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Correct answer

C. 等于零

Principle or equation

零点定理:若函数在闭区间上连续,且端点函数值异号,则至少存在一点使函数值为零。

Why this answer is correct

零点定理保证存在ξ∈(a,b)使得f(ξ)=0。

Example

f(x)=x-1在[0,2]上连续,f(0)=-1,f(2)=1,异号,所以存在ξ=1使f(ξ)=0。

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