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Find the limit as x approaches infinity of 1/x

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Answer
0\boxed{0}

As xx gets larger and larger (like 10,100,100010, 100, 1000), the fraction 1x\frac{1}{x} gets closer and closer to 00.

Problem: Find the limit lim⁡x→∞1x\lim_{x \to \infty} \frac{1}{x}.

Steps

  1. Identify the behavior of the denominator
    As x→∞, the denominator x grows without bound.\text{As } x \to \infty, \text{ the denominator } x \text{ grows without bound.}
  2. Apply the limit law for reciprocals
    lim⁡x→∞1x=0\lim_{x \to \infty} \frac{1}{x} = 0

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