Solve the Initial Value Problem for X as a Function $$\left( 2 t ^ { 3 } - 2 t ^ { 2 } + t - 1 \right) \frac { d x } { d t } = 3 , x ( 2 ) = 0$$

question 117

Multiple Choice

Solve the initial value problem for x as a function of t.
- $$\left( 2 t ^ { 3 } - 2 t ^ { 2 } + t - 1 \right) \frac { d x } { d t } = 3 , x ( 2 ) = 0$$

• A) \(x = \ln | t - 1 | - \frac { 1 } { 2 } \ln \left| t ^ { 2 } + \frac { 1 } { 2 } \right| + \frac { 1 } { 2 } \ln 4.5\)
• B) \(x = \ln | t - 1 | - \sqrt { 2 } \tan ^ { - 1 } \sqrt { 2 } t + \sqrt { 2 } \tan ^ { - 1 } 2 \sqrt { 2 }\)
• C) \(x = \ln | t - 1 | - \tan ^ { - 1 } \sqrt { 2 } t - \ln \left| t ^ { 2 } + \frac { 1 } { 2 } \right| + \tan ^ { - 1 } 2 \sqrt { 2 } + \ln 4.5\)
• D) \(x = \ln | t - 1 | - \sqrt { 2 } \tan ^ { - 1 } \sqrt { 2 } t - \frac { 1 } { 2 } \ln \left| t ^ { 2 } + \frac { 1 } { 2 } \right| + \sqrt { 2 } \tan ^ { - 1 } 2 \sqrt { 2 } + \frac { 1 } { 2 } \ln 4.5\)

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Definitions:

Schemas

Internalized representations of the world that allow individuals to understand and predict their environment.

Piaget

A Swiss psychologist known for his pioneering work in child development, particularly his theory of cognitive development that describes how children develop logical thinking.

Organized Patterns

Structured or systematic arrangements or sequences observed in data, behaviors, or processes.

Egocentrism

A cognitive bias where individuals perceive, interpret, and judge the world primarily from their own perspective.