1. 14.5 Surface Area The equations for these surfaces can be found at http://virtualmathmuseum.org/Surface/gallery_o.html#PseudosphericalSurfaces

2. 1 4.5 Surface Area

3. Recall from Calc BC If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: We need to get dx out from under the radical. Length of Curve (Cartesian)Lengths of Curves:

4. This formula will be proven at the end of the slide show

5. Example 1 Find the surface area of the portion of the plane z = 2 – x – y that lies above the circle in the first quadrant.

6. Example 1 Solution

7. Example 4 Find the surface area of the portion of the hemisphere that lies above region R bounded by the circle

8. Example 4 solution

9. Example 4 solution slide 2

10. A math professor is one who talks in someone else's sleep.

11. Proof of surface area formula slide 1

12. Diagrams for surface area formula