Section 3.3-solutions

# Section 3.3-solutions - troyer(lmt836 Section 3.3...

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troyer (lmt836) – Section 3.3 – isaacson – (55826) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ind the value oF f ( a ) when f ( t ) = 2 t + 3 t + 5 . 1. f ( a ) = - 8 a + 5 2. f ( a ) = - 7 ( a + 5) 2 3. f ( a ) = - 8 ( a + 5) 2 4. f ( a ) = 7 a + 5 5. f ( a ) = 7 ( a + 5) 2 correct 6. f ( a ) = 8 ( a + 5) 2 Explanation: By defnition, f ( a ) = lim h 0 f ( a + h ) - f ( a ) h . Now, For the given f , f ( a + h ) = 2( a + h ) + 3 a + h + 5 , while f ( a ) = 2 a + 3 a + 5 . Thus f ( a + h ) - f ( a ) = 2( a + h ) + 3 a + h + 5 - 2 a + 3 a + 5 = p (2( a + h ) + 3)( a + 5) - ( a + h + 5)(2 a + 3) P ( a + h + 5)( a + 5) . But { 2( a + h ) + 3 } ( a + 5) = 2 h ( a + 5) + (2 a + 3)( a + 5) , and ( a + h +5)(2 a +3) = h (2 a +3)+( a +5)(2 a +3) . Consequently,

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Section 3.3-solutions - troyer(lmt836 Section 3.3...

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