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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 , 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 r 3 where r is the radius. (a) 48 cc/min, (b) 711 cc/min, (c) 1340 cc/min, (d) 768 cc/min, (e) 384 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
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