# What is #F(x) = int e^(x-2) +x^2 dx# if #F(0) = 1 #?

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The integral of ( e^{x-2} + x^2 ) with respect to ( x ) is ( \frac{1}{2} e^{x-2} + \frac{1}{3} x^3 + C ). Given that ( F(0) = 1 ), we can substitute ( x = 0 ) into the expression for the integral and solve for ( C ). Thus, ( 1 = \frac{1}{2} e^{-2} + 0 + C ). Solving for ( C ), we get ( C = 1 - \frac{1}{2} e^{-2} ). Therefore, ( F(x) = \frac{1}{2} e^{x-2} + \frac{1}{3} x^3 + 1 - \frac{1}{2} e^{-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.

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