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Lecture 4 – Arc Length

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Estimate the length of the given through appropriate choices for lower and upper bounds.

Arc Length – curve has a certain length

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Consider one segment out of n pieces and then let n go to infinity.

f(x)

Use more and more hypotenuse lengths to better the approximations.

x

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Find the length of the given curve.

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f(x)

Find the length of the given curve.

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Find the length of the given curve.

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f(x)

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f(x)

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Find the surface area by revolving the curve around the y-axis.

Find the surface area by revolving the curve around the x-axis.

Put the surface areas in decreasing order for the given curve.

A: revolved about the y-axis.

B: revolved about the x-axis.

C: revolved about the line x=2.

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