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Given Quizzes Spring 2008 Each quiz is worth 9 points. Quiz 39 April 24 5 - sec 2 u + 8) du 3u 4 Scores: 9, 9, 9, 9, 9, 7, 7, 6, 6, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0 7 Evaluate (24u - Quiz EC April 22 Use linear approximation to approximate ( 3.02 ) 5 . Scores: 9, 9, 8, 8, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 38 April 21 The radius of a sphere is measured to be 4 feet with an error of 1/3 inch. a. Find the approximate error in the calculated volume of the sphere. b. Find the approximate relative error in the calculated volume of the sphere. 4 3 r Volume of a Sphere: V = 3 Scores: 9, 8, 7, 7, 7, 7, 5, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 37 April 18 If y = 3 x 2 + 15 and x = 7 and x = - 0.1 , then a. use differentials to approximate y , (6 pts.) b. find the approximate relative change in y. (3 pts.) Scores: 9, 9, 9, 7, 6, 6, 6, 5, 4, 1, 1, 0, 0, 0, 0, 0, 0 Quiz 36 April 17 8 - x3 lim Find x 9 x 2 - 64 Scores: 9, 8, 8, 6, 5, 4, 4, 4, 3, 2, 2, 2, 2, 0, 0, 0, 0 Quiz 35 April 15 8 + 2w 3 - 7 w 5 lim 3 Find w - 27 w 5 - 64w 2 Scores: 9, 8, 7, 7, 6, 6, 6, 5, 5, 4, 2, 2, 2, 2, 0, 0, 0 Quiz 34 April 14 2-t lim Find t - 3 + 4 t 2 + 12 t Scores: 9, 6, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 33 April 11 A balloon is released from the ground and rises vertically. An observer on the ground is located 30 meters from the point where the balloon is released. If the angle of elevation from the observer to the balloon is changing at a rate of 3 per second, then how fast is the distance from the balloon to the observer changing when the balloon is 70 meters above the ground? A diagram can be used to identify your variable(s). Scores: 6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 32 April 10 A farmer wishes to fence a rectangular pasture with a total area of 90 square yards, and he wants to divide it into two parts with a fence across the middle. Find the dimensions that would require the least amount of fencing. A diagram can be used to identify your variable(s). Scores: 8, 8, 7, 6, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 31 April 8 Find the volume of the largest cylinder that can be inscribed in a cone with height 9 feet and base radius 4 feet. 2 Volume of a Cone: V = r h Volume of a Cylinder: V = r 2 h 3 Scores: 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 30 April 7 Sketch the graph of a continuous function f given the following information. Plot and label any local maximum and minimum point(s) and inflection point(s). Sign of f (x ) : + -2 Sign of f (x ) : - -1 + 1 - 0 - + 2 - f ( - 2) = 0 , f ( - 1) = - 2 , f (0) = - 4 , f (1) = - 2 , f (2) = 0 Scores: 9, 9, 9, 9, 8, 8, 8, 7, 7, 6, 5, 5, 4, 3, 0, 0, 0, 0, 0 Quiz 29 April 4 If - 3 and 2 are critical numbers of the function h( x) = x 4 - x 3 - 18 x 2 + 24 x - 12 , then use the 4 Second Derivative Test to classify whether there is a local maximum or local minimum occurring at the given critical numbers or whether the test fails. Scores: 9, 9, 8, 8, 8, 8, 7, 5, 5, 3, 3, 3, 3, 0, 0, 0, 0 Quiz EC April 3 Given the function h( x) = x 2 + 39 x + 36 6 x . Then h ( x) = x 2 + 13 x - 12 and 4 x3/ 2 x 2 - 13 x + 36 . Find the following : 8 x5/ 2 a. Interval(s) on which h is concaved downward ____________________ b. Interval(s) on which h is concaved upward ____________________ h ( x) = c. Inflection Point(s) ________________ Scores: 9, 7, 7, 7, 7, 6, 6, 6, 2, 0, 0, 0, 0, 0, 0, 0 Quiz 28 April 1 Given f ( x ) = x 4 - 8 x 3 + 128 x - 14 Sign of f (x) - -2 Sign of f (x) + 0 - 4 + 4 + + Find (a) Local Maximum(s) and (b) Local Minimum(s) Scores: 9, 7, 6, 6, 6, 5, 3, 3, 2, 0, 0, 0, 0, 0 Quiz 27 Mar 31 If g ( x ) = ( x 2 - 5) 3 6 x - 2 , then find a. the interval(s) on which g is decreasing b. the interval(s) on which g is increasing Scores: 9, 8, 7, 6, 6, 3, 3, 3, 3, 3, 3, 2, 2, 2, 0, 0 Quiz 26 Mar 27 8 If s(t ) = is the position function which gives the position (in meters) of a particle at 5 t - 11 time t (in hours), then find the acceleration of the particle when t = 4 hours. Scores: 9, 9, 9, 9, 8, 8, 7, 6, 6, 4, 4, 4, 3, 3, 3, 2, 0 Quiz 25 Mar 25 Differentiate 2 x 3 + x 4 y 2 = x cot y 5 . Scores: 9, 9, 8, 8, 8, 8, 8, 8, 7, 6, 5, 4, 4, 4, 3, 2, 1, 0, 0 Quiz 24 Mar 21 Find the equation (in point-slope form) of the normal line to the graph of y = sin x - 2 csc 7 x at the point for which x = . 6 9, Scores: 8, 7, 6, 5, 5, 3, 3, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0 Quiz 23 Mar 20 Differentiate f (t ) = sec 7 ( 2 t 4 - t ) . Scores: 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 5, 5, 2, 2, 1, 1, 0, 0, 0, 0, 0 Quiz 22 Mar 18 Differentiate y = 5 u + cos u tan 3u - 8u 3 using the Quotient Rule. Do NOT simplify your answer. Scores: 9, 9, 9, 8, 8, 8, 8, 8, 8, 7, 7, 7, 6, 6, 5, 4, 3, 1, 0, 0 Quiz 21 Mar 17 Find the equation (in point-slope form) of the tangent line to the graph of x 4 - 4 x 2 y + 2 y 3 = 10 at the point ( 2 , - 3 ) . Scores: 9, 9, 9, 9, 8, 8, 7, 7, 7, 7, 6, 6, 5, 5, 4, 4, 3, 2, 0, 0, 0, 0 Quiz 20 Mar 13 Differentiate g ( w) = (2 w 4 + 9) (6 - w 2 ) 8 . Simplify your answer. Scores: 9, 9, 9, 9, 8, 8, 7, 6, 6, 5, 5, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0 Quiz 19 Mar 10 Differentiate h(t ) = 3 8t - 9t 6 . Scores: 9, 9, 9, 9, 9, 8, 8, 8, 8, 7, 7, 5, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 18 Feb 29 8 - 7 x - 3 / 2 . Do NOT simplify your answer. 4 3x Scores: 9, 9, 9, 8, 8, 8, 7, 6, 6, 6, 5, 4, 3, 3, 1, 0 Differentiate y = 30 5 x3 + Quiz 17 Feb 28 t 6 - 8t 3 + 9 If s (t ) = is the position function which gives the position (in feet) of a particle at time t (in 4t 3 seconds), then find the velocity of the particle when t = 3 seconds. Scores: 9, 9, 8, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 16 Feb 25 3 x + 12 where the tangent line is horizontal. x 2 + 20 Scores: 9, 9, 7, 7, 7, 7, 6, 5, 4, 3, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0 Find the point(s) on the graph of y = Quiz 15 Feb 22 Find the slope of the normal line to the graph of y = ( x 3 - 4 x 2 - 8 x + 6) (5 + 3 x - 4 x 2 ) at the point for which x = - 1 . Scores: 9, 9, 8, 7, 7, 7, 7, 7, 7, 6, 5, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0 Quiz 14 Feb 21 If s (t ) = 15 + 8 t 3 - 3 t 4 is the position function which gives the position (in yards) of a particle at time t (in minutes), then find the position(s) when the particle is stopped. Scores: 9, 9, 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 3, 3, 3, 3, 3, 2, 1, 0, 0, 0, 0 Quiz 13 Feb 19 Find the equation of the tangent line to the graph of f ( x ) = x 5 - 4 x 3 + 5 x 2 - 3x - 12 at the point for which x = - 2 . Scores: 9, 9, 9, 9, 9, 9, 8, 8, 8, 6, 6, 6, 4, 4, 4, 3, 3, 2, 2, 1, 0, 0 Quiz 12 Feb 18 Use the definition of derivative to find the derivative of the function f ( x ) = Scores: 9, 9, 9, 8, 8, 5, 5, 5, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0 Quiz 11 Feb 15 3x - 8 . a. Use a limit to find the slope of the tangent line to the graph of the function f ( x) = at the point for which x = - 3 . b. Write the equation (in point-slope form) of the tangent line at this point. Scores: 9, 8, 8, 8, 6, 6, 6, 5, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0 Quiz 10 Feb 12 6-t Find tlim 6 t - 6 Scores: 9, 8, 8, 8, 5, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 9 Feb 11 13 - 3 x - 2 x 2 , x < - 4 33 - 4 x , - 4 x 2 , then find lim h( x) . If h( x) = x2 3 x - 9 x + 15 , x > 2 Scores: 8, 8, 8, 7, 7, 7, 7, 7, 6, 6, 4, 4, 4, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 8 Feb 8 Find xlim 3 - x 2 + 3x Scores: 9, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 7 Feb 5 6h 2 - 7 h - 20 Find h lim 2 - 2h 2 + 7 h - 30 Scores: 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 5, 0, 0, 0 Quiz 6 Feb 1 11w - 2 - 8 Find lim w6 w-6 Scores: 9, 9, 9, 9, 9, 9, 7, 7, 3, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 5 Jan 31 4t 2 - 12t Find tlim 2 3 t - 6t + 9 6 4x - 9 Scores: 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 7, 7, 6, 6, 6, 6, 4, 4, 1, 1, 0, 0, 0 Quiz 4 Jan 29 3 x 2 + 20 x + 32 Find x lim 4 - x 2 + 2x - 8 Scores: 9, 9, 9, 9, 9, 8, 8, 7, 7, 7, 7, 7, 6, 5, 5, 5, 4, 2, 2, 2, 1, 0, 0, 0 Quiz 3 Jan 18 An open rectangular box is to be constructed having a volume of 60 cubic inches. The length of the bottom of the box is four times the width of the bottom. Express the amount of material, which is needed to make this box, as a function of one variable. A diagram can be used to identify your variable(s). Scores: 9, 9, 9, 9, 8, 7, 6, 5, 5, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 2 Jan 17 4 g ( x + h) - g ( x ) If g ( x) = , then find . 3x - 5 h Scores: 9, 8, 7, 7, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Quiz 1 Jan 15 16 - 3x . x+2 Scores: 9, 9, 8, 8, 8, 8, 7, 5, 5, 5, 5, 4, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Find the domain of the function h( x) =

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