# How do I find the antiderivative of #f(x)=e^(-2x)#?

You can check your result by deriving it so that you ought to get the original integrand.

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To find the antiderivative of ( f(x) = e^{-2x} ), you can use the power rule for integration. The antiderivative of ( e^{ax} ) with respect to ( x ) is ( \frac{1}{a} e^{ax} + C ), where ( C ) is the constant of integration. Applying this rule to ( f(x) = e^{-2x} ), where ( a = -2 ), we have:

[ \int e^{-2x} , dx = \frac{1}{-2} e^{-2x} + C ]

Simplifying, we get:

[ \int e^{-2x} , dx = -\frac{1}{2} e^{-2x} + C ]

So, the antiderivative of ( f(x) = e^{-2x} ) with respect to ( x ) is ( -\frac{1}{2} e^{-2x} + 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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