Precalculus: Mathematics for Calculus (Standalone Book)
7th Edition
ISBN: 9781305071759
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Brooks Cole
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Chapter 11, Problem 2RE
(a)
To determine
To find: The vertex, focus and directrix of the parabola
(b)
To determine
To sketch: The graph of the parabola
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Find the area between the curves.
x= -2, x = 7, y=2x² +3, y=0
Set up the integral (or integrals) needed to compute this area. Use the smallest possible number
of integrals. Select the correct choice below and fill in the answer boxes to complete your choice.
A.
7
[[2x² +3] dx
-2
B.
[[ ] dx+
-2
7
S [ ] dx
The area between the curves is
(Simplify your answer.)
The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days).
What is the total accumulated growth during the first 2.5 days?
Set up the definite integral that determines the accumulated growth during the first 2.5 days.
2.5
Growth = (105e0.3x) dx
0
(Type exact answers in terms of e.)
Evaluate the definite integral.
Growth=
(Do not round until the final answer. Then round to one decimal place as needed.)
Find the total area of the shaded regions.
y
18-
16-
14-
12-
10-
8-
6-
y=ex+1-e
4-
2-
0-
2
3
4
5
-2
-4-
X
☑
The total area of the shaded regions is
(Type an integer or decimal rounded to three decimal places as needed.)
Chapter 11 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 6ECh. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 8ECh. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...
Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 12ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 50ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 54ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 59ECh. 11.1 - Families of Parabolas (a) Find equations for the...Ch. 11.1 - Parabolic Reflector A lamp with a parabolic...Ch. 11.1 - Satellite Dish A reflector for a satellite dish is...Ch. 11.1 - Suspension Bridge In a suspension bridge the shape...Ch. 11.1 - Reflecting Telescope The Hale telescope at the...Ch. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.2 - An ellipse is the set of all points in the plane...Ch. 11.2 - The graph of the equation x2a2+y2b2=1 with a b 0...Ch. 11.2 - The graph of the equation x2b2+y2a2=1 with a b 0...Ch. 11.2 - Label the vertices and foci on the graphs given...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Prob. 6ECh. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Prob. 8ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 13ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 18ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 32ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 51ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Ancillary Circle The ancillary circle of an...Ch. 11.2 - Prob. 62ECh. 11.2 - Family of Ellipses If k 0, the following equation...Ch. 11.2 - How Wide Is an Ellipse at a Focus? A latus rectum...Ch. 11.2 - Perihelion and Aphelion The planets move around...Ch. 11.2 - The Orbit of Pluto With an eccentricity of 0.25,...Ch. 11.2 - Lunar Orbit For an object in an elliptical orbit...Ch. 11.2 - Plywood Ellipse A carpenter wishes to construct an...Ch. 11.2 - Sunburst Window A sunburst window above a doorway...Ch. 11.2 - DISCUSS: Drawing an Ellipse on a Blackboard Try...Ch. 11.2 - DISCUSS: Light Cone from a Flashlight A flashlight...Ch. 11.2 - DISCUSS: Is It an Ellipse? A piece of paper is...Ch. 11.3 - A hyperbola is the set of all points in the plane...Ch. 11.3 - The graph of the equation x2a2y2b2=1 with a 0, b ...Ch. 11.3 - Prob. 3ECh. 11.3 - Label the vertices, foci, and asymptotes on the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Prob. 6ECh. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Prob. 8ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 10ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 38ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 40ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Perpendicular Asymptotes (a) Show that the...Ch. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Navigation In the figure on the next page, the...Ch. 11.3 - Comet Trajectories Some comets, such as Halleys...Ch. 11.3 - Ripples in Pool Two stones are dropped...Ch. 11.3 - Prob. 59ECh. 11.3 - DISCUSS: Light from a Lamp The light from a lamp...Ch. 11.4 - Prob. 1ECh. 11.4 - The graphs of x2 = 12y and (x 3)2 = 12(y 1) are...Ch. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Prob. 12ECh. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Prob. 20ECh. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 50ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 52ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Path of a Cannonball A cannon fires a cannonball...Ch. 11.4 - Orbit of a Satellite A satellite is in an...Ch. 11.4 - Prob. 68ECh. 11.5 - Suppose the x- and y-axes are rotated through an...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 18ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 26ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Identifying a Hyperbola Using Rotation of Axes (a)...Ch. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11.5 - Prob. 36ECh. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - DISCOVER PROVE: Geometric Invariants Do you...Ch. 11.6 - Prob. 1ECh. 11.6 - Prob. 2ECh. 11.6 - Prob. 3ECh. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - Prob. 6ECh. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - Prob. 11ECh. 11.6 - Prob. 12ECh. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 15ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 17ECh. 11.6 - Prob. 18ECh. 11.6 - Prob. 19ECh. 11.6 - Prob. 20ECh. 11.6 - Prob. 21ECh. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Prob. 25ECh. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Prob. 29ECh. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Perihelion and Aphelion The planets move around...Ch. 11.6 - Prob. 45ECh. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11 - (a) Give the geometric definition of a parabola....Ch. 11 - Prob. 2RCCCh. 11 - (a) Give the geometric definition of a hyperbola....Ch. 11 - Prob. 4RCCCh. 11 - Prob. 5RCCCh. 11 - Prob. 6RCCCh. 11 - Prob. 7RCCCh. 11 - Prob. 8RCCCh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Path of the Earth The path of the earth around the...Ch. 11 - LORAN A ship is located 40 mi from a straight...Ch. 11 - Prob. 67RECh. 11 - Prob. 68RECh. 11 - Prob. 69RECh. 11 - Prob. 70RECh. 11 - Prob. 71RECh. 11 - Prob. 72RECh. 11 - Prob. 73RECh. 11 - Prob. 74RECh. 11 - Prob. 75RECh. 11 - Prob. 76RECh. 11 - Prob. 77RECh. 11 - Prob. 78RECh. 11 - Prob. 79RECh. 11 - Prob. 80RECh. 11 - Find the focus and directrix of the parabola x2 =...Ch. 11 - Prob. 2TCh. 11 - Find the vertices, foci, and asymptotes of the...Ch. 11 - Prob. 4TCh. 11 - Prob. 5TCh. 11 - Prob. 6TCh. 11 - Prob. 7TCh. 11 - Prob. 8TCh. 11 - Prob. 9TCh. 11 - Determine whether the equation represents an...Ch. 11 - Determine whether the equation represents an...Ch. 11 - Prob. 12TCh. 11 - Prob. 13TCh. 11 - Find an equation for the parabola with focus (2,...Ch. 11 - A parabolic reflector for a car headlight forms a...Ch. 11 - (a) Use the discriminant to determine whether the...Ch. 11 - Prob. 17TCh. 11 - Conics in Architecture The photographs on page 836...Ch. 11 - Constructing a Hyperbola In this problem we...Ch. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - Tangent Lines to a Parabola In this problem we...Ch. 11 - Prob. 6P
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