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Unformatted text preview: Calculus I Quiz 4 Block 1, Version 1 McGill University Department of Mathematics & Statistics MATH 140 This is a closed book quiz. Calculators are not allowed. Quiz 4 Version 1 You must fill and return this sheet to get credit. 25 minutes duration SURNAME: GIVEN NAMES: MR, MISS, MS, MRS, &c.: STUDENT NUMBER: This examination has 10 multiple choice questions. They are to be answered on the answer card provided. Correct answers count 4 points, incorrect answers 1 points. Be sure to enter on the answer card: • Your student number. • The version of the exam that you are taking, i.e. version 1. • Your name. • The check code, i.e. the first two letters of your family name. 1. Let f ( x ) = x 5ln( x ) . Then f ( e 5 ) = (a) 50 e 125 , (b) 50 e 120 , (c) 25 e 125 , (d) 25 e 120 , (e) 10 e 125 . 2. Let y = f ( x ) be defined by the equation y + 7 x 2 + xe 4 y = 8 near x = 1, y = 0. The value of f (1) is (a) 15 2 , (b) 3, (c) 7 5 , (d) 14 5 , (e) 0. 3. Let y = f ( x ) be defined by the equation 10 x 3 + 4 xy 7 y 3 = 7 near x = 1, y = 1. The value of f (1) is (a) 13 4 , (b) 3, (c) 27 17 , (d) 0, (e) 2. 4. Let f ( x ) = arcsinh( x ). Then f ( x ) = (a) 1 √ 1 x 2 , (b) 1 x √ 1 + x 2 , (c) x √ x 2 1 , (d) 1 √ 1 + x 2 , (e) 1 √ x 2 1 . 5. The minimum value taken by the function f ( x ) = x 2 + 10 x on [ 9 , 1] is (a) 16, (b) 26, (c) 32, (d) 25, (e) 34. 6. The minimum value taken by the function f ( x ) = 4sin( x ) 5cos( x ) on [0 , π 2 ] is (a) 5, (b) 3, (c) 2, (d) 7, (e) 10. 7. Let f denote the function f ( x ) = (1 + x 2 ) e 3 x defined on [0 , ∞ ). Which answer best describes the location where f takes its absolute minimimum value? (a) x = 0, (b) x = 6, (c) x = 7, (d) x = 1 / 3, (e) minimum not attained. 8. Let f ( x ) = arctan( x ). Then f 00 (3) is (a) 3 / 100, (b) 3 / 50, (c) 3 / 5, (d) 0, (e) 3 / 50. 9. The radius of a sphere is increasing at a rate of 3 cm. per minute. How fast is the volume increasing when the radius is 8 cm.? Note that the volume V of a sphere is given by the formula V = 4 3 πr 3 where r is the radius. (a) 48 π cc/min, (b) 711 π cc/min, (c) 1340 π cc/min, (d) 768 π cc/min, (e) 384 π cc/min. 10. Two sides of a triangle are both increasing at a rate of 7 cm/min and the angle between them is decreasing at a rate of 3 radians per minute.? At what rate is the area increasing when the triangle is equilateral of side 3 √ 3 cm. (a) 171 4 sq. cm./min, (b) 9 sq. cm./min, (c) 45 2 sq. cm./min, (d) 9 2 sq. cm./min, (e) 45 4 sq. cm./min. Calculus I Quiz 4 Block 1, Version 2 McGill University Department of Mathematics & Statistics MATH 140 This is a closed book quiz. Calculators are not allowed. Quiz 4 Version 2 You must fill and return this sheet to get credit. 25 minutes duration SURNAME: GIVEN NAMES: MR, MISS, MS, MRS, &c.: STUDENT NUMBER: This examination has 10 multiple choice questions. They are to be answered on the answer card provided....
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 Fall '10
 Drury
 Given name, Monotonic function, A Closed Book, sq. cm./min

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