Solve the Problem $y = \ln ( \csc x ) , \pi / 6 \leq x \leq \pi / 2$

question 105

Multiple Choice

Solve the problem.
-Find the length of the curve $y = \ln ( \csc x ) , \pi / 6 \leq x \leq \pi / 2$

• A) \(\ln ( \sqrt { 3 } + 2 )\)
• B) \(\ln ( \sqrt { 3 } + 1 )\)
• C) \(\ln ( \sqrt { 3 } )\)
• D) \(1 - \ln ( \sqrt { 3 } + 2 )\)

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Definitions:

Socially Optimal Pricing

Pricing strategies aimed at maximizing societal welfare rather than corporate profits, emphasizing fairness and accessibility.

Marginal Cost

The cost of producing one additional unit of a product, important for decision-making in economics and business.

Fair-return Pricing

Pricing strategy aiming to set prices that are considered fair for consumers while allowing providers a reasonable profit.

Natural Monopoly

A market condition where a single firm can provide a good or service at a lower cost than any potential competitor, leading to exclusive control over the market.