# How do you find the antiderivative of #f(x)=1/4x^4-2/3x^2+4#?

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where c is the constant of integration.

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To find the antiderivative of ( f(x) = \frac{1}{4}x^4 - \frac{2}{3}x^2 + 4 ), integrate each term separately: [ \int \frac{1}{4}x^4 - \frac{2}{3}x^2 + 4 , dx ] [ = \frac{1}{4} \int x^4 , dx - \frac{2}{3} \int x^2 , dx + \int 4 , dx ]

Now, apply the power rule for integration to each term: [ = \frac{1}{4} \left( \frac{1}{5}x^5 \right) - \frac{2}{3} \left( \frac{1}{3}x^3 \right) + 4x + C ]

Combine the terms and add the constant of integration ( C ): [ = \frac{1}{20}x^5 - \frac{2}{9}x^3 + 4x + C ]

So, the antiderivative of ( f(x) = \frac{1}{4}x^4 - \frac{2}{3}x^2 + 4 ) is ( \frac{1}{20}x^5 - \frac{2}{9}x^3 + 4x + C ), where ( C ) is the constant of integration.

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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.

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