The Function $f(x)=e^{-x^{2} / 2}$ Is Part of the Normal Probability Density Function (Or Bell-Shaped

question 25

Multiple Choice

The function $f(x) =e^{-x^{2} / 2}$ is part of the normal probability density function (or bell-shaped curve) .Find the Maclaurin series for $\int e^{-x^{2} / 2} d x$ by first finding the Maclaurin series for $f(x)$ and then integrating it term by term.

• A) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{2 i+1}}{(2 i+1) 2^{i}(i !)}+C\)
• B) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{2 i}}{(2 i) 2^{i}(i !)}+C\)
• C) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{2 i+1}}{(2 i+1) 2^{i}(2 i !)}+C\)
• D) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{2 i}}{(2 i) 2^{i}(2 i !)}+C\)

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Definitions:

Metacognitive Theory

A theory suggesting that people with generalized anxiety disorder implicitly hold both positive and negative beliefs about worrying.

Intolerance Of Uncertainty Theory

An explanation for generalized anxiety disorder that states that certain individuals cannot tolerate the knowledge that negative events may occur, even if the possibility of occurrence is very small.

Unconditional Positive Regard

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Rogers's Client-Centered Theory

A psychological approach developed by Carl Rogers that emphasizes an individual's self-worth and the importance of unconditional positive regard from therapists.