How do you determine if #f(x) =sin(2x)# is an even or odd function?
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To determine if ( f(x) = \sin(2x) ) is an even or odd function, we evaluate ( f(x) ) and compare it with ( f(x) ).

Even function: If ( f(x) = f(x) ) for all ( x ) in the domain of ( f ), then ( f(x) ) is an even function.

Odd function: If ( f(x) = f(x) ) for all ( x ) in the domain of ( f ), then ( f(x) ) is an odd function.
For ( f(x) = \sin(2x) ):
Evaluate ( f(x) ): [ f(x) = \sin(2(x)) = \sin(2x) = \sin(2x) ]
Compare ( f(x) ) with ( f(x) ): [ \sin(2x) \neq \sin(2x) ]
Since ( f(x) ) is not equal to ( f(x) ), the function ( f(x) = \sin(2x) ) is an odd function.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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