Use the Divergence Theorem to Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 146

Multiple Choice

Use the Divergence Theorem to evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } ( x , y , z ) = x ( y + 1 ) \mathbf { i } + 2 y z \mathbf { j } - \left( z ^ { 2 } + y z \right) \mathbf { k }$ and S is the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$ .

• A) \(- 4 \pi\)

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Definitions:

Tukey's

A statistical method, commonly Tukey's range test or Tukey's Honest Significant Difference (HSD) test, used to find means that are significantly different from each other.

LSD

Lysergic acid diethylamide, a potent psychoactive drug, or in a statistical context, it might refer to the Least Significant Difference test for comparing means.

Randomized Block Design

A statistical experimental design that aims to reduce confounding variables by grouping similar experimental units into blocks before randomly assigning treatments within each block.

Sum of Squares for Blocks

Sum of Squares for Blocks is a measure used in analysis of variance (ANOVA) to assess the variance within groups or blocks of a factor in an experimental design.