# How do you find the volume of the solid generated when the regions bounded by the graphs of the given equations #y = 2/sqrtx, x=1, x=5# and the #x#-axis are rotated about the #x#-axis?

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To find the volume of the solid generated by rotating the region bounded by the graphs of the equations (y = \frac{2}{\sqrt{x}}), (x = 1), (x = 5), and the x-axis about the x-axis, you would use the method of cylindrical shells.

The volume can be calculated using the integral:

[ V = 2\pi \int_{1}^{5} x \left(\frac{2}{\sqrt{x}}\right) dx ]

Solving this integral yields the volume of the solid generated by the rotation.

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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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