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 y-values of these intersection points.
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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.
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Calculate the midpoint of the y-values of the intersection points: Once you have (x_1) and (x_2), find the corresponding y-values for each curve. Then, find the midpoint of these y-values, 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 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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