$\"\"$

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The functions are $\"\"$ and $\"\"$ on interval $\"\"$ .

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(a) Label the functions.

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Graph the functions $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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Observe the graph:

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The functions in order of increasing arc length are $\"\"$ and $\"\"$ .

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$\"\"$

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(c) Find the arc lengths of the $\"\"$ and $\"\"$ .

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The functions are $\"\"$ and $\"\"$ on interval $\"\"$ .

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Definition of the arc length:

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If the curve $\"\"$ , $\"\"$ , then the length of the curve is defined as, $\"\"$ .

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Find the derivatives of the functions.

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

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Find the arc length of $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the arc length of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Calculate the arc lengths of $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(a) Graph of the functions $\"\"$ and $\"\"$ :

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$\"\"$

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(b) The functions in order of increasing arc length are $\"\"$ and $\"\"$ .

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