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calculus · worked example

Solve 當 x→2 時 (x²-4)/(x-2) 的極限 = 4

Method: 因式分解後約分. Verified step-by-step solution with our free AI math solver.
Problem

lim⁡x→2x2−4x−2\lim_{x \to 2} \frac{x^2 - 4}{x - 2}

Step-by-step solution

  1. 直接代入得到 00\frac{0}{0} — 不定型。

  2. 將分子以平方差因式分解：x2−4=(x−2)(x+2)x^2 - 4 = (x - 2)(x + 2)。

  3. 約去公因式 (x−2)(x - 2)：lim⁡x→2(x+2)\lim_{x \to 2}(x + 2)。

  4. 代入：2+2=42 + 2 = 4。

Answer

44

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