Lesson #36 Differentials

Quote of the Day: 
   "Mathematics is written for mathematicians." 
      -- Copernicus


Objectives:
    The student will continue to compute differentials.
    The student will apply differentials to computing 
         approximations for roots.


1. Collect homework.

2. To introduce Linear Approximations or Differentials:
      If you stretch a rope tightly around the earth,
      and then increase the length of the rope by about
      6 feet (i.e, you increase the circumference by 6.28
      feet), how far would the rope be above the ground?

      Have students write down their guess.

      Answer is one foot!
       
      How would this change if the rope were tied around a 
      ball that has a diameter of 1 foot?  

      To illustrate, take a piece of string and have 
        students make a circle with it on the floor.
      Then take another piece of string (6 feet 3 inches
        longer than the first) and make a circle outside 
        the first.  Measure the change in the radius.

3. Example
       

4. Ten Commandments of Mathematics

5. Assignment: 
     p. 217 (10, 29, 41) 
     p. 188 (27, 28)
     "Farside" Droodle Worksheet  
     p. 219 (5, 12, 18, 19)   



Click here to go to the next page