# Consider the function #f(x)= -(x-3)^2+4# how do you write an equation using a limit to determine the area enclosed by f(x) and the x-axis?

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To determine the area enclosed by the function f(x) and the x-axis, we can use a definite integral. The integral of f(x) from a to b represents the area enclosed between the curve and the x-axis over the interval [a, b]. In this case, we need to find the limits of integration, which are the x-values where f(x) intersects the x-axis. To find these points, we set f(x) equal to zero and solve for x. In this case, -(x-3)^2+4 = 0. By solving this equation, we can find the x-values where f(x) intersects the x-axis. Once we have these limits of integration, we can evaluate the definite integral to find the area enclosed by f(x) and the x-axis.

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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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