Linear Approximations

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Linear Approximations
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Objectives

• Students will be able to
• Calculate the differential of a function
• Use differentials to approximate values for
  expressions
• Use differentials to approximate change in
  revenue (population, area, volume, and
  tolerances)

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Vocabulary

• Linear Approximation

Differential Form of the Derivative
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Formulas

• Volume of a Cube

Area of a Circle
Volume of a Sphere
Volume of a Cone
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Example 1

• For the function y below, find dy, given x -2
  and ?x 0.1.

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Example 2

• Use the differential to approximate the radical
  expression

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Example 3

• Use the differential to approximate the
  expression

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Example 4

• The demand for grass seed (in thousands of
  pounds) at a price of p dollars is
• Use the differential to approximate the change in
  demand for a change in price from 2 to 2.10.

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Example 5
Beach balls 1 foot in diameter have a thickness
of 0.03 inches. How much material would be
needed to make 5000 beach balls?
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Example 6
A worker is cutting a square from a piece of
sheet metal. The specifications call for an area
that is 16 cm2 with an error of no more than 0.01
cm2. How much error could be tolerated in the
length of each side to endure that the area is
within tolerance?