Use Stokes' Theorem to Evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 47

Multiple Choice

Use Stokes' Theorem to evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$ .
$$\mathbf { F } ( x , y , z ) = 7 \cos x \mathbf { i } + 5 e ^ { y } \mathbf { j } + 2 x y \mathbf { k }$$
$C$ is the curve obtained by intersecting the cylinder $x ^ { 2 } + y ^ { 2 } = 1$ with the hyperbolic paraboloid $z = x ^ { 2 } - y ^ { 2 }$ , oriented in a counterclockwise direction when viewed from above

• A) \(- 2 \pi\)
• B) 0
• C) \(\pi\)
• D) 1

Understand the mechanisms of animal development, including the process of metamorphosis.

Recognize the importance and mechanisms of diversity in animal adaptation to various environments.

Understand the structure and function of specialized animal organs and systems.

Identify the causes and consequences of animal behaviors and physiological processes, including feeding and locomotion.

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Definitions:

Bipolar Cell

A type of neuron found in the eyes that conducts signals from the photoreceptors to the ganglion cells, integral in the visual pathway.

Cone

(1) In botany, a reproductive structure in many gymnosperms that produces either microspores or megaspores. (2) In zoology, one of the conical photoreceptive cells of the retina that is particularly sensitive to bright light and, by distinguishing light of various wavelengths, mediates color vision. Compare with rod.

Compound Eye

A type of eye found in some arthropods, consisting of multiple small visual units that provide a wide field of vision and the ability to detect movement.

Camera Eye

A type of eye found in vertebrates and some mollusks that is characterized by a spherical lens that focuses light on the retina, producing a detailed image.