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final-1004-2008-revised

final-1004-2008-revised - MATH 1004 Final Examination...

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MATH 1004 Final Examination December 2008 1 Multiple-Choice Questions Please choose only one answer and insert in PENCIL in your Scantron sheet. 1. [3 marks] Evaluate lim x 0 sin 8 x 16 x . (a) 1 (b) 1 / 2 (c) 3 / 2 (d) 0 2. [4 marks] Let f ( x ) = Arctan x 2 + 1. Evaluate f (1). (Note that Arctan x and tan 1 x represent the same function). (a) f (1) = 1 3 (b) f (1) = 1 2 (c) f (1) = 1 3 2 (d) f (1) = 1 3. [3 marks] Let f ( x ) = 2 | x + 1 | + 1. Calculate L = lim h 0 f ( 1 + h ) f ( 1) h . 4. [4 marks] Find the derivative of the function f defined by f ( x ) = x 3 x . (a) 3 x 3 x (1 + ln x ) (b) 3 x 3 x 1 (c) 3 x 3 x (d) x 3 x (1 + 2 ln x )
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2 MATH 1004 Final Examination December 2008 5. [3 marks] A differentiable function f with a differentiable inverse, F , has the property that f (1) = 1 / 2 and f (1) = 1 / 2. What is the value of the derivative of the inverse of f at x = 1 / 2? That is, calculate F (1 / 2). 6. [3 marks] Let f ( x ) = 5 x +1 . Evaluate f (8). In other words, find the derivative of f at x = 8.
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