How do you determine if #1/(x^3+1)# is an even or odd function?
Evaluate
We find:
So this function is neither even nor odd.
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To determine if ( \frac{1}{x^3+1} ) is an even or odd function, we can use the properties of even and odd functions:
 An even function satisfies ( f(x) = f(x) ) for all ( x ) in the domain.
 An odd function satisfies ( f(x) = f(x) ) for all ( x ) in the domain.
Now, let's analyze ( \frac{1}{x^3+1} ) for even or odd behavior:

Substitute ( x ) into the function: [ f(x) = \frac{1}{(x)^3+1} = \frac{1}{x^3+1} ]

Compare ( f(x) ) with ( f(x) ): [ f(x) = \frac{1}{x^3+1} ] [ f(x) = \frac{1}{x^3+1} ]
Since ( f(x) = \frac{1}{x^3+1} ) is not equal to ( f(x) = \frac{1}{x^3+1} ), the function ( \frac{1}{x^3+1} ) does not satisfy the condition for being an even function.
Now, let's check if it's an odd function: [ f(x) = \frac{1}{x^3+1} ] [ f(x) = \frac{1}{x^3+1} ]
Since ( f(x) = \frac{1}{x^3+1} ) is equal to ( f(x) = \frac{1}{x^3+1} ), the function ( \frac{1}{x^3+1} ) satisfies the condition for being 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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