[Solved] Why does the error function erf(x) approach 1 as x approaches infinity? — Ans: Because it represents the integral of the Gaussian probability density function... | SciPy

SciPy - Constants and Special Functions

Why does the error function erf(x) approach 1 as x approaches infinity?

ABecause erf is a periodic function with maximum 1

BBecause erf is a polynomial that grows without bound

CBecause it represents the integral of the Gaussian probability density function over the entire real line

DBecause erf(x) is defined to be 1 for all large x

Step-by-Step Solution

Solution:

Step 1: Understand erf definition
erf(x) is defined as the integral of 2/sqrt(pi) * exp(-t^2) from 0 to x.
Step 2: Behavior as x approaches infinity
As x -> ∞, the integral covers the entire positive half of the Gaussian curve, approaching total area 1.
Final Answer:
Because it represents the integral of the Gaussian probability density function over the entire real line -> Option C
Quick Check:
erf integral approaches 1 as x -> ∞ [OK]

Quick Trick: erf(x) -> 1 because it integrates Gaussian PDF fully [OK]

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