Show That the Function Has Exactly One Zero in the Given

question 110

Essay

Show that the function has exactly one zero in the given interval.
- $$r ( \theta ) = 5 \cot \theta + \frac { 1 } { \theta ^ { 2 } } + 6 , ( 0 , \pi )$$

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Definitions:

Market Portfolio

A theoretical portfolio of investments that contains all available assets in the market, representing the entire market.

Single-Index Model

A simplified way to model the returns of a security or portfolio with respect to the returns of the overall market, using only the market index as the explanatory variable.

Systematic Risk

The risk inherent to the entire market or market segment, also known as non-diversifiable risk or market risk.

Market Index

A statistical measure that tracks the performance of a basket of specific stocks, representing a portion of the overall market to reflect trends or market health.