Part 7: Summary

1. What is a surface? (Give as general a description as you can of this concept, in your own words.)
2. Give a one-sentence description of each of the ways to picture a surface that we have used in this module.
   
   
3. What does the graph of x² + y² = 1 look like in three dimensional space? How is this different from the graph of x² + y² + z² = 1?
   
   
4. How is the graph of the function f(x,y) = x² + y² different from the graphs in question 3? What do the level curves of this graph look like? How are the level curves different from the level curves of the graphs in question 3?
   
   
5. What does a "patch" of surface look like when you zoom in near a point on the surface? (You can try this with any of the examples in your worksheet.) Does your answer hold for all points on any surface? What about the vertex of a cone?
   

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