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Lecture 4 – Arc Length

Lecture 4 – Arc Length . Estimate the length of the given through appropriate choices for lower and upper bounds. Arc Length – curve has a certain length. 4. 4. 3. 3. 2. 2. 1. 1. Lengths (in general). Consider one segment out of n pieces and then let n go to i nfinity. f(x).

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Lecture 4 – Arc Length

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  1. Lecture 4 – Arc Length Estimate the length of the given through appropriate choices for lower and upper bounds. Arc Length – curve has a certain length 4 4 3 3 2 2 1 1

  2. Lengths (in general) 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

  3. Example 1 4 Find the length of the given curve. 3 2 1

  4. Example 2 f(x) Find the length of the given curve. 1 x 1 2

  5. Example 3 Find the length of the given curve. 2 f(x) 1 x

  6. Example 3 – continued 2 f(x) 1 x

  7. Lecture 5 – Surface Area Find the surface area by revolving the curve around the y-axis.

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

  9. Example 1 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.

  10. Example 1-continued 4 4 4 3 3 3 2 2 2 1 1 1

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