Calculus > QUESTIONS & ANSWERS > Practice_midterm_solutions Harvard University - MATH 2413S (All)

Practice_midterm_solutions Harvard University - MATH 2413S

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Solutions to practice midterm. 1. (10 points) Determine whether the following are TRUE or FALSE, and write your answer into the box. You will receive 2 points for a correct answer and 0 points for a ... n answer left blank. a) A curve is given in polar coordinates (r; θ) by the equation θ = 30. The plot of this curve in Cartesian coordinates (x; y) is a line passing through the origin. TRUE b) There is a value m such that the angle between the vectors h2; 1; −1i and h0; m; 1i is 45◦. FALSE c) There is a vector ~v and a value m 6= 0, such that h2; −3; 1i × ~v = h0; 0; mi. FALSE d) The vector h−1; 2; 8i is orthogonal to the line through the points P (10; 0; 3) and Q(6; 2; 2). TRUE e) If the partial derivatives fx(x; y) and fy(x; y) exist at a point (x; y), then the function f(x; y) is continuous at this point. FALSE [Show More]

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