How do you determine if #x-sin(x)# is an even or odd function?
Examine how it acts on
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To determine if the function ( f(x) = x - \sin(x) ) is even or odd:
- For an even function, ( f(-x) = f(x) ) for all ( x ) in the domain.
- For an odd function, ( f(-x) = -f(x) ) for all ( x ) in the domain.
For ( f(x) = x - \sin(x) ):
- Test for evenness: ( f(-x) = (-x) - \sin(-x) = -x + \sin(x) )
- Test for oddness: ( -f(x) = - (x - \sin(x)) = -x + \sin(x) )
Since ( f(-x) = f(x) ), the function ( f(x) = x - \sin(x) ) is even.
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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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