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Unformatted text preview: Fundamentals of Engineering MATHEMATICS REVIEW Exercises Youre Supposed to know this stuff! Review Format FE sample math questions will be posted on the screen with multiple choice answers. Write down your answer and raise your hand; or if you have a question, stand up . Answer will be posted after most have answered and other questions can be asked by standing up. Select the best answer The partial derivative of is: a. b. c. d. x y ) ( 6 3 2 2 z x x z z x y 6 3 2 2 z xz z zx z x 6 6 2 9 2 x 6 6 2 z x Answer The partial derivative of is: a. b. c. d. x y ) ( 6 3 2 2 z x x z z x y 6 3 2 2 z xz z zx z x 6 6 2 9 2 x 6 6 2 z x If the functional form of a curve is known, differentiation can be used to determine all of the following EXCEPT the a. Concavity of the curve b. Location of the inflection points on the curve c. Number of inflection points on the curve d. Area under the curve between certain bounds. If the functional form of a curve is known, differentiation can be used to determine all of the following EXCEPT the a. Concavity of the curve b. Location of the inflection points on the curve c. Number of inflection points on the curve d. Area under the curve between certain bounds. Which of the following choices is the general solution to this differential equation ? a. b. c. d. ; 5 y dt dy 1 ) ( y t e 5 t e 5 t e 5 t e 5 5 Which of the following choices is the general solution to this differential equation ? a. Assume y = exp( t) b. ( + 5)exp( t) = 0, c. d. ; 5 y dt dy 1 ) ( y t e 5 t e 5 t e 5 t e 5 5 If D is the differential operator, then the general solution to ( D + 2) 2 y = 0 is: a. b. c. d. x e C 4 1 x e C 2 1 x C C e x 2 1 4 x C C e x 2 1 2 If D is the differential operator, then the general solution to ( D + 2) 2 y = 0 is: a. b. c. d. x e C 4 1 x e C 2 1 x C C e x 2 1 4 x C C e x 2 1 2 Multiple identical roots D 2 + 4 D + 4 = 0 Then has only one root, i.e. Assume that y(x) = u(x)e2x = u v. Then y = uv + uv and y = uv + vu + 2 uv, so (v+4v+4v)u + uv + 2uv+4uv = 0 and v = 2v, leaving u = 0; thus u = C 1 x + C 2 x Ce y 2 2 4 4 4 4 2 A particle traveled on a straight line in such a way that the distance S from a given point on that line after time t was S = 20 t 3 t 4 . The rate of change of acceleration at time t = 2 is: a. 72 b. 144 c. 192 d. 208 A particle traveled on a straight lin in such a way that the distance S from a given point on that line after time t was S = 20 t 3 t 4 . The rate of change of acceleration at time t = 2 is: a. 72 b. 144 c. 192 d. 208 The rate of change of acceleration is called jerk and is the third derivative w.r.t. time. Which of the following is a unit vector perpendicular...
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This note was uploaded on 10/26/2010 for the course ME 401 taught by Professor Hao during the Spring '10 term at Old Dominion.
 Spring '10
 Hao

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