Infinity Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Evaluate lim⁡x→0+1x2\lim_{x \to 0^+} \frac{1}{x^2}.

Solution

  1. 1
    As x→0+x \to 0^+, x2→0+x^2 \to 0^+ (small positive number).
  2. 2
    Dividing 1 by an arbitrarily small positive number gives an arbitrarily large number.
  3. 3
    Therefore the limit is +∞+\infty.

Answer

+∞+\infty
This is an infinite limit (not a limit at infinity). As xx approaches 0 from the right, x2x^2 becomes tiny and positive, making 1/x21/x^2 grow without bound. The limit does not exist as a finite real number.

About Infinity

A concept representing a quantity that grows without bound — infinity is not a real number but a description of unbounded behavior.

Learn more about Infinity →

More Infinity Examples

Example 1 easy

Evaluate [formula].

Example 2 medium

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Example 3 easy

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