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Reviewed CSCA STEM Chinese question · Standard

在微积分中,函数 f(x) 在点 x₀ 处的导数定义为:当自变量的增量 Δx 趋于零时,函数值的增量 Δy 与 Δx 之比的_。

  1. 极限
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Correct answer

A. 极限

Principle or equation

导数的定义:f'(x₀) = lim(Δx→0) [f(x₀+Δx)-f(x₀)]/Δx,即增量之比的极限。

Why this answer is correct

导数是一个极限值,不是简单的和、积或差。

Example

对于 f(x)=x²,f'(x)=lim(Δx→0) [(x+Δx)²-x²]/Δx = lim(Δx→0)(2x+Δx)=2x。

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