Find the Taylor Series for the Given Function at the Indicated

question 15

Multiple Choice

Find the Taylor series for the given function at the indicated point $x = a \text {. }$ $f ( x ) = e ^ { 2 x } + e ^ { - 2 x }$ ; a = 0

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { 2 \left( 2 ^ { 2 n } \right) } { ( 2 n ) ! } x ^ { 2 n }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { 2 \left( 2 ^ { n } \right) } { n ! } x ^ { 2 n }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { 2 \left( 2 ^ { 2 n + 1 } \right) } { ( 2 n + 1 ) ! } x ^ { 2 n + 1 }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { 2 \left( 2 ^ { n } \right) } { n ! } x ^ { n }\)

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Definitions:

Sum-Of-The-Years'-Digits Depreciation

An accelerated depreciation method that allocates a proportionally higher depreciation in the early years of an asset's life and less in the later years, based on a fraction determined by the asset's useful life.

Economic Life

The period over which an asset is expected to be usable for its intended purpose.

Inflation On Fixed Assets

The impact of rising prices (inflation) on the purchasing power and value of fixed assets over time, affecting their replacement cost and depreciation calculations.

GAAP

Generally Accepted Accounting Principles, a set of accounting standards, guidelines, and procedures used in the United States for financial reporting.