Differentials

• Find dy for y = 5x² - 10
• Approximate  using differentials
• Write down the function to be used:  
• Choose an x close to 2 that is a perfect square (an easy y-value to calculate)
  x = 100
• Then , x = 100, y = 10
• Find y ', using differentials:  
• Substitute known values:
  
• Add dy to the known y-value:  y = 10 + .1 = 10.1
• Terms for error propogation

• The measurement of the circumference of a circle is found to be 56 centimeters.

• Approximate the percentage error in computing the area of the circle if the possible error in measuring the circumference is 1.2 centimeters.
  
  The percentage error is   3    (100)  =  4.286 %
                                       70
• Estimate the maximum allowable percentage error in measuring the circumference if the error in computing the area cannot exceed 3%.