$\"\"$

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The curve is $\"\"$ .

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(a)

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Graph the curve $\"\"$ on interval $\"\"$ .

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Graph:

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$\"\"$ .

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$\"\"$

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(b)

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The curve is $\"\"$ .

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The polygon with one side $\"\"$ join the line segment between $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The one end point of the line segment is $\"\"$ .

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

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$\"\"$

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$\"\"$

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The other end point of the line segment is $\"\"$ .

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The length of curve is $\"\"$ .

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$\"\"$

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The polygon with two sides $\"\"$ is the line segments between $\"\"$ , $\"\"$ and $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The one end point on the line segment is $\"\"$ .

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The arc length is $\"\"$ .

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The polygon with four sides $\"\"$ is the line segments between $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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

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$\"\"$

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$\"\"$

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The point is $\"\"$ .

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

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$\"\"$

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$\"\"$

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The point is $\"\"$ .

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The arc length is $\"\"$ .

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$\"\"$

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$\"\"$

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(c)

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The curve is $\"\"$ and the interval is $\"\"$ .

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Length of the curve $\"\"$ on the interval $\"\"$ is $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The length of the curve is $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Length of the curve is $\"\"$ .

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$\"\"$

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(d)

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Length of the curve is $\"\"$ .

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$\"\"$

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$\"\"$

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Using calculator the value of $\"\"$ .

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The length of the curve is approximately $\"\"$ is larger than other approximations.

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The length of the curve using polygons with sides $\"\"$ are small when compared to $\"\"$ .

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$\"\"$

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(a) Graph of the curve $\"\"$ on interval $\"\"$ :

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$\"\"$ .

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

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$\"\"$

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(c) Length of the curve is $\"\"$ .

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(d) The length of the curve using polygons with sides $\"\"$ are small when compared to $\"\"$ .