What are some examples of a symmetric function?
A symmetric function is a function in several variable which remains unchanged for any permutation of the variables.
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Some examples of symmetric functions include:
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Even functions: Functions where ( f(x) = f(-x) ) for all ( x ) in the domain. Examples include ( f(x) = x^2 ) and ( f(x) = \cos(x) ).
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Odd functions: Functions where ( f(x) = -f(-x) ) for all ( x ) in the domain. Examples include ( f(x) = x^3 ) and ( f(x) = \sin(x) ).
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Functions symmetric about the y-axis: Functions where ( f(x) = f(-x) ) for all ( x ) in the domain. Examples include ( f(x) = |x| ) and ( f(x) = x^4 - 2x^2 + 1 ).
These functions exhibit various types of symmetry that can be visualized graphically or algebraically.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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