Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as $ t $ increases.

$ x = e^{-a} + t $, $ \quad y = e^a - t $, $ \quad -2 \leqslant t \leqslant 2 $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

GRAPH AND TABLE

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

16:57

In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.

01:59

Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).

01:22

Sketch the curve by using …

01:38

02:59

0:00

02:22

04:08

03:36

Use point plotting to grap…

(a) Sketch the curve by us…

03:21

The problem is sketch a drift by using the parametric efficients to plot points indicated with an arrow. The direction invites curve is traced, as t increases. So first i we come here. Values of x and y and t is equal to negative 2 x is equal to e to negative 8 minus 2 point y is equal to e to a plus 2 t, and t is equal to negative 1 x is e to negative. A minus 1 y is 2 negative e to 8, plus 1 by t is equal to 0 x is e to negative. A y is c to a when t is equal to 1 x is e to negative. A plus 1 y is e to a minus 1 point, and t is equal to 2 x is e to negative. A plus 2 y is e to a minus 2 point. Then we can sketch the curve as follows: first x, equal to e to negative a minus 2 y is equal to e to a plus twoso. It cascatch like here some point here and into negative a minus y into a plus 1 here and into negative a into a and e to negative, a plus 1 into a minus 1 and e to negative a plus 2 into a minus 2 here. So this is a curve by using the parametric equations to plot point, and its arrow is a direction in which securis traced, as increases.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:47

Determine the domain and range for the graph below: Write your answer In Int…

05:53

The industrial process that is used to convert fuel to gasoline caried out a…

Your company receives shipments of 200 Printed Circuit Boards (PCBs) from a …

04:28

8 AFlag 0 question 2Hf € X= cost; Y I sint; 2 AFA Ithen 2xydh 20 1 p…

02:52

There is a new diagnostic test for a disease that occurs in about 0.10% of t…

01:54

Call centers typically have high turnover: The director of human resources f…

02:45

The results of a national survey showed that on average, adults sleep 7.2 ho…

01:27

22. Suppose that factory 4 produces 12 tables and 6 chairs an hour while fac…

06:50

What is the Cartesian equation describing the path particle whose position i…

02:13

The accompanying table provides the data for 100 room inspections at each of…