Find the number #b# such that the line y=b divides the region...?
Find the number #b# such that the line y=b divides the region bounded by the curves #y=x^2# and #y=4# into two regions with equal area.
Find the number
Find the area of the region first.
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To find the number (b) such that the line (y = b) divides the region enclosed by the curves (y = x^2  4x + 3) and (y = 3  x^2) into two regions of equal area, we need to set up and solve an equation.
Let's denote the points of intersection of the two curves as (x_1) and (x_2). Then, (b) will be the midpoint of the yvalues of these intersection points.

Find the intersection points: Set the two equations equal to each other and solve for (x): [x^2  4x + 3 = 3  x^2] Solve for (x) to find the intersection points.

Calculate the midpoint of the yvalues of the intersection points: Once you have (x_1) and (x_2), find the corresponding yvalues for each curve. Then, find the midpoint of these yvalues, which will be (b).
This value of (b) will be the number such that the line (y = b) divides the region enclosed by the curves into two regions of equal area.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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