Find the Exact Value of the Expression, If Possible $\sin \left( \tan ^ { - 1 } x \right)$

question 328

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\sin \left( \tan ^ { - 1 } x \right)$

• A) \(\frac { x \sqrt { x ^ { 2 } + 1 } } { x ^ { 2 } + 1 }\)
• B) \(\frac { x \sqrt { x ^ { 2 } - 1 } } { x ^ { 2 } - 1 }\)
• C) \(x \sqrt { x ^ { 2 } + 1 }\)
• D) \(\frac { \sqrt { x ^ { 2 } + 1 } } { x ^ { 2 } + 1 }\)

Understand the concept of budget constraints and opportunity cost.

Interpret production possibilities tables and curves.

Grasp the distinction between normative and positive economics.

Comprehend the concept of utility and how it guides consumer choice.

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Definitions:

Substitute Factor

A factor or input that can be used in place of another to produce a good or service.

Factor Production

Refers to the inputs or resources used in the process of producing goods and services, including land, labor, capital, and entrepreneurship.

Labor Demand Curve

A graphical depiction of the relationship between the quantity of labor that employers wish to hire and the wage rate, assuming other factors are constant.

Marginal Product

The increase in output resulting from an additional unit of input, while keeping other inputs constant.