Let F(x) = X

question 261

Essay

Let f(x) = x
Use a Riemann sum with four subintervals of equal length (n = 4) to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals.
__________ sq units
Repeat previous part with eight subintervals of equal length (n = 8).
__________ sq units
Compare the approximations obtained in previous parts with the exact area (2 sq units). Do the approximations improve with larger n?

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Definitions:

Gender Differences

Variations in characteristics, behaviors, or attitudes between males and females, often shaped by biological, social, and cultural factors.

Play Behavior

Activities performed for self-amusement that have behavioral, social, and psychomotor benefits, often observed in children and young animals.

Strange Situation

A research method used in developmental psychology to assess attachment styles in children by observing their reactions when separated and reunited with their caregivers.

Attachment Style

Patterns of bonding that form between a child and caregiver, influencing emotional and social development and relationships later in life.