advertisement

MAT021C - Spring Quiz 3 - 04.30.15 Name: Student Id: Show all work clearly and in order. Circle your final answers. Justify your answers algebraically whenever possible. Problem 1. Consider the function 1 , (k constant) (1 + x)k a. Find the second order Taylor polyomial (P2 (x)) of f at a = 0. b. For k = 3, find the values of x in the interval [0, 1] such that the error of the second order approximation will be less than 10−2 . f (x) = Problem 2. Sketch the triangle with vertices A(−1, 2, 1), B(1, −1, 3), and C(3, 4, 5). Find its perimeter. Problem 3. Find the center and the radius of the sphere x2 + y 2 + z 2 − 6y + 10z − 30 = 0 Find the point of the sphere that is the nearest to the xy-plane