oldmidterm1

# oldmidterm1 - [3 Answer 2 FULL-SOLUTION PROBLEMS In...

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Student number Name [SURNAME(S), Givenname(s)] MATH 100 (Section 103) Midterm Test 1(X) 2009 Oct 09 This is a closed book examination: no books, notes, electronic memory or communication de- vices are allowed. CALCULATORS AND CELL PHONES ARE NOT ALLOWED. Use backs of pages if necessary, but label clearly. 1. SHORT ANSWER QUESTIONS. If an answer box is provided, put your answer in it, but show your work also. Each question is worth 3 marks, but not all questions are of equal diFculty. At most 1 mark will be given for an incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers. Marks (a) Evaluate (or determine that the limit does not exist) [3] lim x 3 x 2 - 9 x 2 - 6 x + 9 . Answer (b) Evaluate (or determine that the limit does not exist) [3] lim x →∞ 2 x 3 + 5 x x 3 - x 2 + 4 . Answer

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(c) Evaluate (or determine that the limit does not exist) lim x 0 x 2 sin 2 5 x . [3] Answer (d) Diferentiate e 3 x 2 . [3] Answer (e) Determine ( g/f ) 0 (3), iF g (3) = 1, g 0 (3) = - 2, f (3) = 4, f 0 (3) = - 3. [3] Answer (F) ±ind the second derivative oF e - x cos x and simplify your answer

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Unformatted text preview: . [3] Answer 2 FULL-SOLUTION PROBLEMS. In questions 2–4, justify your answers and show all your work. If you need more space, use the back of the previous page. 2. Carefully prove that 2 x 4-x 3 + 2 x 2-1 has a root between x =-1 and x = 1. [5] 3. Use the defnition of the derivative to prove that if f ( x ) is a diFerentiable function [6] and g ( x ) = x 2 f ( x ), then g ( x ) = x 2 f ( x ) + 2 x f ( x ). No credit will be given for using the Product Rule. 3 4. Find a point on the curve y = 16-x 2 that is below the x-axis, such that the tangent [5] line through that point also passes through the point (5 , 0), or determine that no such point exists. 5. Let [6] f ( x ) = ( ax + b if-∞ < x ≤ 2, c + ( x-2) 2 sin ± 1 ( x-2) 2 ² if 2 < x < ∞ , and determine all values (if any exist) of the constants a , b , and c so that f ( x ) is continuous for all x . (Remember to justify your answer.) 4...
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oldmidterm1 - [3 Answer 2 FULL-SOLUTION PROBLEMS In...

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