Use Taylor's Theorem to Find the First Four Terms of the Series

question 8

Multiple Choice

Use Taylor's Theorem to find the first four terms of the series solution of $y ^ { tt } + e ^ { x } y ^ {t } - ( \sin x ) y = 0$ given the initial conditions $y ( 0 ) = - 5$ , and $y ^ { t } ( 0 ) = 7$ and use it to calculate $y \left( \frac { 1 } { 4 } \right)$ . Round your answer to three decimal places.

• A) \(y = - 5 + \frac { 7 } { 1 ! } x - \frac { 5 } { 2 ! } x ^ { 2 } - \frac { 7 } { 3 ! } x ^ { 3 } + \cdots , y \left( \frac { 1 } { 4 } \right) \approx - 3.424\)
• B) \(y = - 5 + \frac { 7 } { 1 ! } x - \frac { 5 } { 2 ! } x ^ { 2 } + \frac { 7 } { 3 ! } x ^ { 3 } + \cdots ; y \left( \frac { 1 } { 4 } \right) \approx - 3.388\)
• C) \(y = - 5 + \frac { 7 } { 1 ! } x - \frac { 21 } { 2 ! } x ^ { 2 } - \frac { 10 } { 3 ! } x ^ { 3 } + \cdots , y \left( \frac { 1 } { 4 } \right) \approx - 3.932\)
• D)\(y = - 5 + \frac { 7 } { 1 ! } x - \frac { 7 } { 2 ! } x ^ { 2 } + \frac { 5 } { 3 ! } x ^ { 3 } + \cdots , y \left( \frac { 1 } { 4 } \right) \approx - 3.456\)
• E)\(y = - 5 + \frac { 7 } { 1 ! } x - \frac { 7 } { 2 ! } x ^ { 2 } - \frac { 5 } { 3 ! } x ^ { 3 } + \cdots ; y \left( \frac { 1 } { 4 } \right) \approx - 3.482\)

Recognize the importance of dividends, interest, and rents as forms of capital income.

Grasp the fundamental economic concept of investment and how it affects capital.

Understand the relationship between savings decisions and investment capabilities of firms.

Know the implications of owning common stock and the benefits it entails.

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Definitions:

Fixed Costs

Business expenses that remain constant regardless of the level of production or business activity, such as rent, salaries, and loan payments.

Cross Elasticity

A measure of how the demand for one good responds to a change in the price of another good.

Normal Good

A good for which demand increases as the income of consumers increases, and falls when consumer income decreases.

Quantity Demanded

The total amount of a good or service that consumers are willing and able to purchase at a given price in a specified time period.