January 22, 2014
6-6
Differentials:
Linear Approximation
Example 2
For
Example 1
For
find dy, given x = 5 and Δx = 0.2
Example 3
find dy, given x = 2 and Δx = -0.06
Use the differential to approximate the radical expression. Then use a calculator
to approximate the quantity, and give the absolute value of the difference in the
two results to 4 decimal places.
Example 4
Example 5
Use the differential to approximate the radical expression. Then use a
calculator to approximate the quantity, and give the absolute value of the
difference in the two results to 4 decimal places.
A company estimates that the revenue (in dollars) from the sale of x
doghouses is given R(x) = 13,000 ln(0.01x + 1). Use the differential to
approximate the change in revenue from the sale of one more doghouse if 80
doghouses have already been sold.
January 22, 2014
Example 7
Example 6
A cube 6 inches on an edge is given a protective coating 0.3 inch thick. About
how much coating should a production manager order for 1000 such cubes?
The population of bacteria (in millions) in a certain culture x hours after an
experimental nutrient is introduced into the culture is
Use the differential to approximate the changes in population for the following
changes in x.
a) 2 to 2.5
b) 6 to 6.25
Example 8
Example 10
The shape of a colony of bacteria on a Petri dish is circular. Find the
approximate increase in its area if its radius increases from 40 mm to 46 mm.
A spherical snowball is melting. Find the approximate change in volume if the
radius decreases from 4 cm to 3.8 cm.