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Linear Approximations

Linear Approximations. 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). Vocabulary. Linear Approximation.

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Linear Approximations

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  1. Linear Approximations

  2. 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)

  3. Vocabulary Linear Approximation Differential Form of the Derivative

  4. Formulas Volume of a Cube Area of a Circle Volume of a Sphere Volume of a Cone

  5. Example 1 For the function y below, find dy, given x = -2 and Δx =0.1.

  6. Example 2 Use the differential to approximate the radical expression

  7. Example 3 Use the differential to approximate the expression

  8. 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.

  9. 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?

  10. 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?

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