MA1014_HW1_201012

MA1014_HW1_201012 - Mathematics II Homework

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Mathematics for Engineering II Homework I: Differentials fpm@itesm.mx Linear approximation formula: f ( x 0 + Δ x ) = f ( x ) = f ( x 0 ) + ʹ f ( x 0 )( x x 0 ) Solved example: Find the approximate value of the square root of 99: 1. Identify the function: f ( x ) = x 2. Identify the value that, when substituted in the function, is easy to calculate. x 0 =100 (because the square root of 100 is 10) 3. The value you are asked to calculate is x , so x = 99 3. Calculate ʹ f ( x ) = 1 2 x 1 2 = 1 2 x 4. Substitute back into the linear approximation formula: f (99) = f (100) + ʹ f (100)(99 100) , therefore, 99 = 100 + 1 2 100 ( 1) that is, 99 = 10 1 20 99 = 199 20 If you compare this result (approximately 9.95) with the number given by a calculator, you will notice that both are almost the same. Now, try to solve the following exercises. Solutions appear in at the end of this document.
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This note was uploaded on 12/26/2010 for the course MT 1014 taught by Professor Franciscoperez during the Fall '10 term at ITESM.

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MA1014_HW1_201012 - Mathematics II Homework

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