The Fourier Series of the Function $f ( x ) = x$

question 35

Multiple Choice

The Fourier series of the function $f ( x ) = x$ on $[ - 1,1 ]$ is

• A) \(\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } 2 \cos ( n \pi x ) / ( n \pi )\)
• B) \(\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n + 1 } 2 \cos ( n \pi x ) / ( n \pi )\)
• C) \(\sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n } 2 \sin ( n \pi x ) / ( n \pi )\)
• D) \(\sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } 2 \sin ( n \pi x ) / ( n \pi )\)
• E) \(\sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \sin ( n \pi x ) / ( n \pi )\)

Distinguish between the concepts of diffusion, creative destruction, and technological advancements.

Understand the impact of technological advancements on allocative and productive efficiency.

Recognize the different sources of R&D financing, including venture capital and retained earnings, and their relevance to firm size.

Understand the economic implications of the interest-rate cost-of-funds curve on R&D financing.

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Definitions:

Average Tax Rate

The proportion of total income that is paid as tax.

Total Income

Refers to the aggregate amount of all revenue sources over a given period, including wages, salaries, benefits, and earnings from investments.

Total Taxes

The cumulative amount of taxes paid by an individual or company to federal, state, and local governments.

Average Tax Rate

The ratio of the sum of taxes paid to the overall income, determined by dividing the total taxes paid by the total income.