Let Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 118

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = \frac { x \mathbf { i } + y \mathbf { j } + z \mathbf { k } } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } }$ . Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where C is the curve of intersection of the paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$ and the cylinder $x ^ { 2 } + y ^ { 2 } = 2 x$ .

• A) \(1\)
• B)\(- 1\)
• C)\(\sqrt { 2 }\)
• D)\(- \sqrt { 2 }\)
• E)\(\sqrt { 3 }\)
• F)\(- \sqrt { 3 }\)
• G)\(2\)
• H)\(0\)

Distinguish between fixed, variable, and total costs in business operations.

Evaluate decision-making processes in operational and financial contexts.

Understand the concept of average cost and how it is affected by changes in the quantity of units produced and workers hired.

Learn about the relationship between marginal cost (MC), marginal revenue (MR), and their impact on hiring and production decisions.

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