What is #f(x) = int x^2e^(x-1)-x^3e^-x dx# if #f(2) = 7 #?
your integral is given by
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To find ( f(x) = \int x^2e^{x-1} - x^3e^{-x} , dx ) given ( f(2) = 7 ), you can evaluate the integral and solve for the constant of integration using the given initial condition. The integral of ( x^2e^{x-1} ) and ( x^3e^{-x} ) can be computed separately using integration by parts. Then, substitute ( x = 2 ) into the expression for ( f(x) ) and solve for 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.
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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