If $x = \frac { 2 \sin t } { 1 + \cos t }$

question 100

Multiple Choice

If $x = \frac { 2 \sin t } { 1 + \cos t }$ , find $\frac { d x } { d t }$ .

• A) \(\frac { 1 } { 2 + \cos t }\)
• B) \(\frac { 2 } { 1 + \cos t }\)
• C) \(\frac { 2 \cos t } { 1 + \sin t }\)
• D) \(\frac { 2 \cos t } { ( 1 + \cos t ) ^ { 2 } }\)

---

Definitions:

Expected Utility Maximizer

An individual who makes choices under uncertainty to maximize their expected level of satisfaction, based on the probabilities of different outcomes.

Von Neuman-Morgenstern

A theory in economics that provides an axiomatic basis for expected utility theory, which helps to explain choice under uncertainty.

Probability

An indication of how probable an event is to happen, represented numerically between 0 and 1, with 0 meaning it cannot happen and 1 meaning it is certain to happen.

Risk Loving

A financial term describing an individual or entity's preference for taking risks, where the potential for higher gains outweighs the possibility of losses.