Infinity Math Example 2

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

Example 2

medium
Evaluate lim⁡x→∞2x3−x5x2+3\lim_{x \to \infty} \frac{2x^3 - x}{5x^2 + 3}.

Solution

  1. 1
    The degree of the numerator (3) is greater than the degree of the denominator (2).
  2. 2
    Divide by x2x^2 (highest power in denominator): 2x−1/x5+3/x2\frac{2x - 1/x}{5 + 3/x^2}.
  3. 3
    As x→∞x \to \infty, the numerator 2x−1/x→∞2x - 1/x \to \infty and denominator →5\to 5.
  4. 4
    Therefore the limit is ∞\infty.

Answer

∞\infty
When the degree of the numerator exceeds the degree of the denominator in a rational function, the limit as x→∞x \to \infty is ±∞\pm\infty — the function grows without bound. The limit does not exist as a finite 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

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Example 3 easy

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Example 4 medium

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