calc notes lecture 20

calc notes lecture 20 - 5 t = to 6 t = 3 Example 3 Find the...

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Lecture Section Objectives Assignment 20 3.8 Differentials and Marginal Analysis 3.8: 1-15 odd, 21, 23, 26, 42 Understanding Goals: 1. Understand the definition of differentials of functions and when to use it. 2. Understand how to use differentials to approximate changes and how to use it to solve real-life problems. 1
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Example 1 : Let 2 y x = . Find dy when 1 x = and 0.01 dx = . Compare this value with y for 1 x = and 0.01 x ∆ = . 2
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Example 2 : A state game commission introduces 50 deer into newly acquired state game lands. The population N of the herd can be modeled by 10(5 3 ) 1 0.04 t N t + = + where t is the time in years. Use differentials to approximate the change in the herd size from
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Unformatted text preview: 5 t = to 6 t = . 3 Example 3 : Find the differential dy of the given functions. a) 2 y x = b) 2 3 3 y x = c) 1 y x x = + d) 1 y x x = + e) 2 1 y x = + 4 ( ) ( ) f x x f x y + ∆-= ∆ Example 4 : The radius of a ball bearing is measured to be 0.7 inch. If the measurement is correct to within 0.01 inch, estimate the propagated error in the volume V of the ball bearing. The relative error in the volume is defined to be the ratio of dV to V . 5 Example 5 : Use differentials to approximate 3 26 . 6...
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This note was uploaded on 04/17/2008 for the course MAT 111 taught by Professor Fan during the Spring '08 term at Union.

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calc notes lecture 20 - 5 t = to 6 t = 3 Example 3 Find the...

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