How do you know if # f(x)=x^2+sin x# is an even or odd function?
In the question:
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To determine if ( f(x) = x^2 + \sin(x) ) is an even or odd function, we can apply the following tests:
- Even function: If ( f(-x) = f(x) ) for all ( x ) in the domain of the function, then the function is even.
- Odd function: If ( f(-x) = -f(x) ) for all ( x ) in the domain of the function, then the function is odd.
For the function ( f(x) = x^2 + \sin(x) ):
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To test for evenness, we substitute ( -x ) into the function: [ f(-x) = (-x)^2 + \sin(-x) = x^2 - \sin(x) ]
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To test for oddness, we substitute ( -x ) into the function and compare it to ( -f(x) ): [ -f(x) = -(x^2 + \sin(x)) = -x^2 - \sin(x) ]
Comparing ( f(-x) ) with ( f(x) ) and ( -f(x) ), we see that neither ( f(-x) = f(x) ) nor ( f(-x) = -f(x) ) holds true.
Therefore, ( f(x) = x^2 + \sin(x) ) is neither an even nor an odd function.
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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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