Find the Length of the Curve $x = \frac { 1 } { 3 } \left( y ^ { 2 } + 2 \right) ^ { \frac { 3 } { 2 } } , 1 \leq y \leq 2$

question 178

Multiple Choice

Find the length of the curve $x = \frac { 1 } { 3 } \left( y ^ { 2 } + 2 \right) ^ { \frac { 3 } { 2 } } , 1 \leq y \leq 2$

• A)0
• B) \(\frac { 7 } { 3 }\)
• C)2
• D) \(\frac { 14 } { 3 }\)
• E)1
• F) \(\frac { 5 } { 3 }\)
• G)4
• H) \(\frac { 10 } { 3 }\)

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Definitions:

Diminishing Returns

A principle stating that if one factor of production is increased while others remain constant, the overall returns will eventually decrease after a certain point.

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An increase in the production of economic goods and services, compared from one period of time to another, often measured by GDP.