$\"\"$

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The inequalities are $\"\"$ , $\"\"$ and $\"\"$ .

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(a) Find the area of the region satisfying the inequalities.

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Area of the region between two curves is $\"\"$ .

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Area of the region is $\"\"$ .

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$\"\"$

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The inequalities are $\"\"$ , $\"\"$ and $\"\"$ .

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(b) Find the volume of the solid generated by revolving the region about $\"\"$ axis.

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Disk method:

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The volume of the solid of revolution is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The volume of the solid is $\"\"$ .

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$\"\"$

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The inequalities are $\"\"$ , $\"\"$ and $\"\"$ .

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(c) Find the volume of the solid generated by revolving the region about $\"\"$ axis.

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Shell method:

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The volume of the solid of vertical revolution is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply L hospital rule to find the limit.

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$\"\"$

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$\"\"$ .

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The volume of the solid is $\"\"$ .

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The volume of the solid about $\"\"$ axis is $\"\"$ .

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$\"\"$

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(a) Area of the region is $\"\"$ .

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(b) The volume of the solid about $\"\"$ axis is $\"\"$ .

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(c) The volume of the solid about $\"\"$ axis is $\"\"$ .