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Unformatted text preview: Create assignment, 57321, Homework 4, Feb 15 at 10:17 pm 1 This printout should have 19 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC3h03s 49:05, calculus3, multiple choice, > 1 min, wordingvariable. 001 The figure below shows the graphs of three functions: t One is the graph of the position function s of a car, one is its velocity v , and one is its acceleration a . Identifywhichgraphgoeswith which function. 1. s : v : a : correct 2. s : v : a : 3. s : v : a : 4. s : v : a : 5. s : v : a : 6. s : v : a : Explanation: Experience tells us that the car is (i) moving forwards when its velocity is positive, (ii) moving backwards when its velocity is negative, (iii)speedingupwhenitsvelocityispositive and increasing, i.e. , when both velocity and acceleration are positive, (iv) slowing down when its velocity is pos itive but decreasing, i.e. , when its velocity is positive but its acceleration is negative. Now v = ds dt a = dv dt , so we need to look at the slope of the tangent line to three graphs to determine which graph is that of position, that of velocity and that of acceleration. Inspection of the graphs thus shows that s : v : a : . keywords: velocity, acceleration CalC3h07b 49:05, calculus3, multiple choice, > 1 min, wordingvariable. 002 Find the second derivative of f when f ( x ) = 3cos2 x 5cos 2 x. 1. f 00 ( x ) = 22sin2 x 2. f 00 ( x ) = 22sin2 x 3. f 00 ( x ) = 11sin2 x 4. f 00 ( x ) = 22cos2 x 5. f 00 ( x ) = 11cos2 x Create assignment, 57321, Homework 4, Feb 15 at 10:17 pm 2 6. f 00 ( x ) = 22cos2 x correct Explanation: Differentiating once we see that f ( x ) = 6sin2 x + 10sin x cos x. Now 2sin x cos x = sin2 x, so f ( x ) = 11sin2 x. Consequently, after differentiating again we obtain f 00 ( x ) = 22cos2 x . keywords: second derivative, trig function CalC3h08a 49:05, calculus3, multiple choice, > 1 min, wordingvariable. 003 Determine d 2 y/dx 2 when x 2 + 3 y 2 = 2 . 1. d 2 y dx 2 = 2 9 y 3 correct 2. d 2 y dx 2 = 2 9 y 3 3. d 2 y dx 2 = 2 9 y 2 4. d 2 y dx 2 = 2 9 y 2 5. d 2 y dx 2 = 1 9 y 3 Explanation: Differentiating implicitly with respect to x we see that 2 x + 6 y dy dx = 0 , which after simplification becomes dy dx = 1 3 x y . But then d 2 y dx 2 = d dx ‡ 1 3 x y · = µ 3 y 3 x dy dx 9 y 2 ¶ = 1 9 y 2 ‡ 3 y + x 2 y · . Consequently, d 2 y dx 2 = 1 9 y 3 ‡ x 2 + 3 y 2 · = 2 9 y 3 . keywords: implicit differentiation, second derivative CalC3h30a 49:05, calculus3, multiple choice, > 1 min, wordingvariable. 004 Determine f ( n ) ( x ) when f ( x ) = 1 1 + 2 x . 1. f ( n ) ( x ) = ( 1) n 2 n n ! (1 + 2 x ) n +1 correct 2. f ( n ) ( x ) = 2 n n !...
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This note was uploaded on 03/20/2008 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas.
 Spring '06
 McAdam

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