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