How do you determine if #f(x) = 6x^5 5x# is an even or odd function?
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To determine if a function is even or odd, we need to check its symmetry.

Even function: A function ( f(x) ) is even if ( f(x) = f(x) ) for all ( x ) in the domain. In other words, if the function is symmetric about the yaxis.

Odd function: A function ( f(x) ) is odd if ( f(x) = f(x) ) for all ( x ) in the domain. In other words, if the function is symmetric about the origin.
For the function ( f(x) = 6x^5  5x ):

Even or odd? Let's first check if it is even or odd. We evaluate ( f(x) ):
( f(x) = 6(x)^5  5(x) )
( f(x) = 6x^5 + 5x )

Check for even: If ( f(x) = f(x) ), the function is even. However, ( f(x) \neq f(x) ), so the function is not even.

Check for odd: If ( f(x) = f(x) ), the function is odd. From our earlier evaluation, ( f(x) = 6x^5 + 5x ), and ( f(x) = 6x^5 + 5x ). Since ( f(x) = f(x) ), the function is odd.
Therefore, ( f(x) = 6x^5  5x ) 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.
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