$\"\"$

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The force of a hydraulic cylinder is $\"\"$ .

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The force is proportional to square of $\"\"$ is $\"\"$ .

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$\"\"$ , $\"\"$ is a constant and $\"\"$ is the distance that the cylinder is extended by in its cycle.

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The domain of $\"\"$ is $\"\"$ .

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(a) Find $\"\"$ as a function of $\"\"$ .

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The value of $\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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The force function $\"\"$ .

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$\"\"$

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(b) Find the average force exerted by the press over the interval $\"\"$ .

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Average value of the function $\"\"$ on $\"\"$ is defined as $\"\"$ .

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In this case $\"\"$ and $\"\"$ .

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The force function $\"\"$ .

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The average value is $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ N.

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The average force is $\"\"$ N. $\"\"$

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(a). The force function $\"\"$ .

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(b). The average force is $\"\"$ N.