The Fourier Series of the Function $f ( x ) = x ^ { 2 }$

question 28

Multiple Choice

The Fourier series of the function $f ( x ) = x ^ { 2 }$ on $[ - 1,1 ]$ is

• A) \(\sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \sin ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right) + \sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \cos ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• B) \(\sum _ { n = 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \sin ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• C) \(\sum _ { n = 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \cos ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• D) \(1 / 3 + \sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \sin ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• E) \(1 / 3 + \sum _ { n - 1 } ^ { \infty } 4 ( - 1 ) ^ { n } \cos ( n \pi x ) / \left( n ^ { 2 } \pi ^ { 2 } \right)\)

Recognize the environmental settings favorable for different types of metamorphism.

Understand the relationship between metamorphism and tectonic settings such as subduction zones and continental rifts.

Identify the geological features associated with faults, including how they can indicate the presence of a fault.

Describe the structural features that can form in association with faults, including folds, cleavage, and shear zones.

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