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:

Normal Credit Balance

Refers to the expected balance type (credit) for certain accounts in accounting, such as revenues, liabilities, and equity accounts.

Liabilities

Financial obligations or debts that a company is required to pay in the future.

Revenues

The total income generated by a company from its business activities, typically from the sale of goods and services to customers.

Common Stock

A type of security representing ownership in a corporation, giving holders a share of profits in the form of dividends and voting rights in corporate matters.