(A) Estimate $\ln 2 = \int _ { 1 } ^ { 2 } \frac { 1 } { x } d x$

question 139

Essay

(a) Estimate $\ln 2 = \int _ { 1 } ^ { 2 } \frac { 1 } { x } d x$ using Simpson's Rule with n = 4.(b) Estimate the error of the approximation in part (a).(c) How large should we take n to guarantee that the estimate by Simpson's Rule is accurate to within 0.001?

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Definitions:

Bond Prices

The market price for which a bond is bought or sold, influenced by interest rates, credit quality, and other factors.

Interest Rate Movements

Fluctuations in the interest rate over time which can affect borrowing costs and investment returns.

Stock and Bond Markets

Financial markets where shares of publicly held companies are issued and traded, and where debt securities are bought and sold.

Rates of Return

A measure of the profit or loss of an investment over a specified period, usually expressed as a percentage of the initial investment.