Let $f ( x , y ) = x ^ { 2 } y$

question 81

Multiple Choice

Let $f ( x , y ) = x ^ { 2 } y$ , and let $R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ . Let R be its own partition, and let $\left( x _ { 1 } ^ { * } , y _ { 1 } ^ { * } \right)$ be the center of R. Calculate the double Riemann sum of f.

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

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Definitions:

Right Angles

A measure of angle which is exactly 90 degrees, indicating a perpendicular relationship between two lines or planes.

Perfect Complements

Two goods with right-angle indifference curves.

Indifference Curves

Indifference curves are graphical representations in microeconomics that indicate different combinations of two goods between which a consumer is indifferent, reflecting their preferences and utility.

Right Angles

An angle measuring exactly 90 degrees.