section 6-1 continued slope fields. definition a slope field or directional field for a...
TRANSCRIPT
![Page 1: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/1.jpg)
Section 6-1 continuedSlope Fields
![Page 2: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/2.jpg)
Definition
• A slope field or directional field for a differentiable equation
is a collection of short line segments with the same slope as the solution curve through a given point (x,y)
),(' yxFy
![Page 3: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/3.jpg)
Definition• A slope field shows the general shape of all
the solutions of a differential equation
![Page 4: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/4.jpg)
yxy '6. Sketch a slope field for
for the points (-1, 1) (0, 1) and (1, 1)
![Page 5: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/5.jpg)
yxy 2'7. Sketch a slope field for
through the point (1, 1)x -2 -2 -1 -1 0 0 1 1 2 2
y -1 1 -1 1 -1 1 -1 1 -1 1
y’=2x+y
![Page 6: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/6.jpg)
A slope field or direction field consists of line segments with slopes given by the differential equation. These line segments give a visual perspective of the slopes of the solutions of the differential equation.
a)Sketch using pencil two approximate solutions of the differential equation on the given slope field, one of which passes through the indicated pointb)Use integration to find the particular solution of the differential equation and use a graphing calculator to graph the solutionc)Compare results with part (a)
Instructions
![Page 7: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/7.jpg)
a) Sketch two possible solutions, one through the point ( -1 , 3)
12 xdx
dy8.
![Page 8: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/8.jpg)
3,112 xdx
dy
b) Integrate to find the general solution
![Page 9: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/9.jpg)
c) Graph solution using graphing calculator
![Page 10: Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f2b5503460f94c45caf/html5/thumbnails/10.jpg)
Assignment
Practice worksheet 6-1