calculus · worked example

Solve lim x→∞ لـ 1/x

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Problem

limx1x\lim_{x \to \infty} \frac{1}{x}

Step-by-step solution

  1. عندما يكبر xx، يتقلص 1x\frac{1}{x} نحو 00.

  2. لأي ε>0\varepsilon > 0، اختر N=1/εN = 1/\varepsilon، عندئذٍ x>N1/x<εx > N \Rightarrow |1/x| < \varepsilon.

  3. إذن limx1x=0\lim_{x \to \infty} \frac{1}{x} = 0.

Answer

00

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