University:
Whitman College
Course:
MATH-225 | Calculus III
Academic year:

2010
Views:

119

Pages:

1
Author:

Francis Spencer

Group Work, Section 10.1 1. Give a parameterization for the line that moves between the points (1, 2) and (−3, −6). 2. Are any of the following graphs (in the (x, y) plane) actually a line? Show that your answer is true by finding either y as a function of x, or x as a function of y: (a) x = t2 , y = t3 , −1 ≤ t ≤ 1. (b) x = t − 1, y = t + 4 (c) x = et − 1, y = et + 4 (d) x = 1 + 3t, y = 2 − t2 3. Try to plot the following set of parametric equations: x(t) = sin(2t) y(t) = cos(t) 0 ≤ t ≤ 2π 4. If x, y are each plotted below, find parametrizations in t for them, and plot the graph of the parametric equations. Figure 1: Graphs of x (left) and y (right), where each is in terms of t. 5. Give a parameterization of the path of a particle of the form: x(t) = a1 cos(a2 t) y(t) = a3 sin(a4 t) 0 ≤ t ≤ 2π so that the particle moves around a circle three times CW (with a radius of 2) starting at (−2, 0). What does the curve look like if a1 = 1, a3 = 3, a2 = a4 = 1? 1

Calculus III Exam 2 Sample Solutions 2010

Related Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock