What is #f(x) = int xe^(2-x) -2 x^2 +2 dx# if #f(0 ) = 2 #?
So:
So:
So:
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To find ( f(x) = \int xe^{2-x} - 2x^2 + 2 , dx ) given that ( f(0) = 2 ), we need to first find the antiderivative of the given function. Then, we can use the given initial condition to determine the constant of integration. Integrating the function ( xe^{2-x} - 2x^2 + 2 ) with respect to ( x ) gives ( -xe^{2-x} - 2/3 x^3 + 2x + C ), where ( C ) is the constant of integration. Using the given condition ( f(0) = 2 ), we find ( C = 2 ). Therefore, ( f(x) = -xe^{2-x} - 2/3 x^3 + 2x + 2 ).
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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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