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Unformatted text preview: h )P (3) h = lim h → 100 + 30(3 + h ) + 4(3 + h ) 2(100 + 30 × 3 + 4 × 3 2 ) h = lim h → 30 h + 24 h + 4 h 2 h = lim h → (54 + 4 h ) = 54 , thus the rate of growth is 54 / month. 1 2 THE DERIVATIVE Example 3. The cost (in dollars) of producing x units of a certain commodity is C ( x ) = 3000 + 5 x + 0 . 02 x 2 . (1) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 101. (2) Find the rate of change of the cost with respect to x when x = 100. Solution (1) Average rate of change is given by C (101)C (100) 101100 = 9 . 04 (2) Rate of change when x = 100 is given by P (100) = lim h → P (100 + h )f (100) h = lim h → 3000 + 5(100 + h ) + 0 . 02(100 + h ) 2(3000 + 5 × 100 + 0 . 02 × 100 2 ) h = lim h → 5 h + 4 h + 0 . 02 h 2 h = lim h → (9 + 0 . 02 h ) = 9...
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 Fall '09
 BenedictGross
 Derivative, Slope, Limits, lim, lim h0

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