Let $f ( x , y ) = x y$ , and Let

question 13

Multiple Choice

Let $f ( x , y ) = x y$ , and let $R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ . Let R be partitioned into four subrectangles by the lines $x = \frac { 1 } { 2 }$ and $y = \frac { 1 } { 2 }$ , and let $\left( x _ { i } ^ { * } , y _ { j } ^ { * } \right)$ be the upper right corner of Rij. Calculate the double Riemann sum of f.

• A) \(\frac { 3 } { 16 }\)
• B) \(\frac { 1 } { 4 }\)
• C) \(\frac { 5 } { 16 }\)
• D) \(\frac { 3 } { 8 }\)
• E) \(\frac { 7 } { 16 }\)
• F) \(\frac { 1 } { 2 }\)
• G) \(\frac { 9 } { 16 }\)

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Definitions:

Esteem Needs

A concept from Maslow's hierarchy of needs that refers to the human desire for respect, self-esteem, and recognition from others.

Deficit Principle

The concept that suggests individuals are more motivated by their unmet needs than by desires that have already been satisfied.

Maslow's Theory

A psychological theory proposing a hierarchy of human needs that motivate behavior, starting from basic physiological needs to self-actualization.

Self-Actualization Needs

The apex of Maslow's needs pyramid, which encompasses achieving one's ultimate potential, pursuing self-realization, aiming for personal development, and experiencing life's high points.