Calculus > EXAM > Harvard University - MATH 2413Midterm1_v2_solution (All)

Harvard University - MATH 2413Midterm1_v2_solution

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Midterm I - Accelerated multivariable calculus - v2 October 13th, 2020 NAME: Instructions: • Time for test: 75 minutes. • You are allowed to write on one sheet of paper useful formulas and ha ... ve it with you during the exam. • Calculators are not allowed. Page 1 of 71. True/False questions: circle T or F. Each question is worth 4 points if you answer correctly, 0 points if you don’t. You receive 2 points if you don’t circle neither T or F. a) F The tangent line to r1(t) = ht; 2t2; −t3i at the point (1; 2; −1) is perpendicular to the tangent line to r2(t) = ht; t + 1; ln ti at the point (1; 2; 0). b) F If r(t) = hsin t; cos t; t3i, then the unit tangent vector is T(t) = hcos t; − sin t; 3t2i. c) T The intersection of the plane defined by the equation 2x − 2y + z − 3 = 0 and of the line defined by the parametric equation 8<: x = t + 2 y = −t + 3 t 2 R z = −3t − 2 is a point. d) F Consider the curve in the plane given by the equation y = x3 + x. Its curvature at the point (1; 2) is equal to 1=3. e) T If the curve r(s) is parametrized with respect to arc length then necessarily: jr0(s)j [Show More]

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