Solutions to Homework Assignment 9
5. Notice that y = (x - 1)2 , so this is the parabola y = x2 shifted right 1 unit. r (t) =< 1, 2t > . At t = 1, this is < 1, 2 > . The graphs are below. The position vector is blue and the tangent vector is green. 6
Solutions to Homework Assignment 8
3. lim t ln t = lim + +
t0 t0
9. Notice that y 2 + z 2 = 1, so the curve lies on that cylinder. This will be a helix revolving around the x-axis every units (instead of 2 because of the 2t inside the sine and cosi
Solutions to Homework Assignment 6
MATH 249-01 and -02 Section 12.7, Page 842 3, 7, 9, 10, 15, 20, 31-36, 37-47 odd, 48, 49, 53, 56 3. Find the graph in the back of the book. I will express the point in rectangular coordinates. x = 2 cos(/4) = 2, y
Solutions to Homework Assignment 7
1. (a) It represents a parabola. (b) It represents a vertical parabolic cylinder. (c) This is also a parabolic cylinder with its vertex along the x-axis. 3. This is independent of x, so it is a cylinder along the x-
Solutions to Homework Assignment 1
MATH 249-01 and -02 Section 12.1, Page 797 1-9, 11, 15-18, 23-33 odd, 35-38, 41 2.
10
5 -10 -5 5 10 -5 00 0 -5
-10
5 10
-10
4. The length of the diagonal is
5. We will see in Section 12.5 that this is an equa