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HW 15 Solutions

# HW 15 Solutions - Derivative Algebraic Homework Solutions...

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Derivative: Algebraic Homework Solutions STOR 112 1. 10.6.6 f 0 ( - 2) = f ( - 2 + h ) - f ( - 2) h as h gets close to 0 = 2( - 2 + h ) 2 + ( - 2 + h ) - (8 - 2) h = - 7 h + 3 h 2 h = ( - 7 + 3 h ) now set h=0 = - 7 Alternatively, this can be written mathematically as follows: f 0 ( - 2) = lim h 0 f ( - 2 + h ) - f ( - 2) h = lim h 0 2( - 2 + h ) 2 + ( - 2 + h ) - (8 - 2) h = lim h 0 - 7 h + 3 h 2 h = lim h 0 ( - 7 + 3 h ) = - 7 10.6.8 f 0 (0) = f (0 + h ) - f (0) h as h gets close to 0 = - h - h 2 h = - 1 - h now set h=0 = - 1 1

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Alternatively, this can be written mathematically as follows: f 0 (0) = lim h 0 f (0 + h ) - f (0) h = lim h 0 - h - h 2 h = lim h 0 - 1 - h = - 1 10.6.10 f 0 (1) = lim h 0 f (1 + h ) - f (1) h = lim h 0 (1 + h ) - 2(1 + h ) 3 - (1 - 2) h = lim h 0 1 + h - 2 - 6 h - 6 h 2 - 2 h 3 + 1 h = lim h 0 - 5 h - 6 h 2 - 2 h 3 h = lim h 0 ( - 5 - 6 h - 2 h 2 ) = - 5 10.6.12 f 0 (5) = lim h 0 f (5 + h ) - f (5) h = lim h 0 2 / (5 + h ) - (2 / 5) h = lim h 0 10 - 2(5 + h ) 5 h (5 + h ) = lim h 0 - 2 h 5 h (5 + h ) = lim h 0 - 2 5(5 + h ) = - 2 25 2
10.6.14 f 0 (12) = lim h 0 f (12 + h ) - f (12) h = lim h 0 (12 + h/k ) - b - (12 /k - b ) h = lim h 0 12 /k + h/k - b - 12 /k + b h = lim h 0 h/k h = lim h 0 1 /k = 1 /k 10.6.16 f 0 ( x ) = lim h 0 f ( x + h ) - f ( x ) h = lim h 0 ( x + h ) 2 - 3 - ( x 2 - 3) h = lim h 0 x 2 + 2 xh + h 2 - 3 - x 2 + 3 h = lim h 0 2 xh + h 2 h = lim h 0 (2 x + h ) = 2

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HW 15 Solutions - Derivative Algebraic Homework Solutions...

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