$\"\"$

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The inner circumference of the ring is $\"\"$ .

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(a)

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The circumference is $\"\"$ .

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$\"\"$

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$\"\"$

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Inner radius of the ring is $\"\"$ .

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$\"\"$

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(b)

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The circumference vary from $\"\"$ and $\"\"$ .

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The circumference is $\"\"$ .

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If Circumference is $\"\"$

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$\"\"$

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$\"\"$

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Inner radius of the ring is $\"\"$

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If Circumference is $\"\"$

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$\"\"$

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$\"\"$

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Inner radius of the ring is $\"\"$ .

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$\"\"$

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(c)

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At $\"\"$ the circumference of the ring is $\"\"$ .

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$\"\"$ .

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Prove the limit $\"\"$ using $\"\"$ definition.

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For each $\"\"$ ,there exists a $\"\"$ such that $\"\"$ whenever $\"\"$ .

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Consider $\"\"$

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$\"\"$

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Consider $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Observe the relationship between two absolute values $\"\"$ and $\"\"$ . $\"\"$ .

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Therefore $\"\"$ .

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$\"\"$ then $\"\"$ .

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$\"\"$

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(a) Inner radius of the ring is $\"\"$ .

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(b) Inner radius of the ring is $\"\"$ when circumference is $\"\"$ .

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Inner radius of the ring is $\"\"$ when circumference is $\"\"$ .

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(c) $\"\"$ and $\"\"$ .