How do you find the area in the first quadrant between the graphs of #y^2=(x^3)/3# and #y^2=3x#?

Answer 1

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Answer 2

To find the area in the first quadrant between the graphs of (y^2 = \frac{x^3}{3}) and (y^2 = 3x), you need to first find the points of intersection between the two graphs by solving the system of equations. Then, integrate the positive difference of the upper and lower curves with respect to (x) from the leftmost intersection point to the rightmost intersection point to find the area. The integral expression for the area is:

[A = \int_{x_1}^{x_2} (y_2 - y_1) , dx]

Where (x_1) and (x_2) are the x-coordinates of the intersection points, and (y_1) and (y_2) are the y-values of the respective curves at a given (x) value.

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Answer from HIX Tutor

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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