MATH 114 Midterm: MATH 114 UPenn m114 sExam 2 Exam

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turquoisegnu128

31 Jan 2019

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Math 114 sample final exam 2: consider the line that is tangent to the cycloid given by the parametric equations x = sin , y = 1 cos , at = . At what point (0, y) does this line meet the y-axis? (b) (0, 2 1) (f) (0, 2 . 10: consider the set of points given in cylindrical coordinates by r = 4 cos . The part of this plane in the rst octant, together with the three coordinate planes, bounds a tetrahedron. What is the volume of this tetrahedron? (a) 8 (b) 9: a vector parallel to the direction of fastest increase of w = 3x2 xy + z starting. 0z 1: evaluate z 1 y2 (a) e 1 (e) e + 1 (b) (f) 3 ln 4 ln 5 yex2 dxdy. (b) 1 (f) 1. 2 (e + 1) (c) 1 (g) 1.

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Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed