The Solution of the Previous Three Problems Is $\sum _ { n = 1 } ^ { \infty } c _ { n } X _ { n } ( x ) e ^ { - \lambda _ { n } k t }$

question 28

Multiple Choice

The solution of the previous three problems is $\sum _ { n = 1 } ^ { \infty } c _ { n } X _ { n } ( x ) e ^ { - \lambda _ { n } k t }$ , where $X _ { n }$ and $\lambda _ { n }$ are given in the previous problem and

• A) \(c _ { n } = \int _ { 0 } ^ { L } f ( x ) d x\)
• B) \(c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x\)
• C) \(c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x / \int _ { 0 } ^ { L } X _ { n } ( x ) d x\)
• D) \(c _ { n } = \int _ { 0 } ^ { L } X _ { n } ^ { 2 } ( x ) d x / \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x\)
• E) \(c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x / \int _ { 0 } ^ { L } X _ { n } ^ { 2 } ( x ) d x\)

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Definitions:

Unwanted Behaviors

Actions or reactions that are considered inappropriate, undesirable, or not in accordance with social norms or personal expectations.

Virtual Reality Exposure Therapy

A therapeutic technique that uses simulated environments within virtual reality to expose individuals to situations related to their psychological issues in a controlled manner.

Aversive Conditioning

A form of behavior therapy that involves repeated association of an undesired behavior with an unpleasant stimulus to reduce the behavior.

Double-blind Procedure

A study design in which neither the participants nor the experimenters know who is receiving a particular treatment, to prevent bias in research results.