Construct the Taylor Polynomial Approximation of Degree 3 to the Function

question 14

Short Answer

Construct the Taylor polynomial approximation of degree 3 to the function $f(x)=\arctan x$ about the point x = 0.Use it to approximate the value $f(0.35)$ to 5 decimal places.How does the approximation compare to the actual value?

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Definitions:

Contraction

The downturn of the business cycle, when real GDP is declining.

Recovery Phase

A period within the economic cycle where activity rebounds following a recession, characterized by increasing GDP, employment, and investment.

Expansion

In economics, expansion refers to a phase of the business cycle where the economy grows and output increases, often characterized by rising employment and income.

Recession Phase

A temporary downturn in the economy, observed through decreased industrial and commercial pursuits, typically observed by a GDP decline in two consecutive quarters.