This is the idea of a slope field graph: 1. Our goal is to sketch the unknown function y (t). 2. We are given a differential equation that allows us to calculate slope values of y (t). 3. We sketch short line segments that have the correct slopes at many points in the plane. These are tangent lines. 4. Follow the flow of the short line segments to sketch a function y (t). Our y (t) sketch must never cross a tangent line, and it should have slopes that are aligned with the tangent line segments. Consider the differential equation y' = y+¤ ·e¯² +1. Steps 1, 2, and 3 have been completed and the result is shown here: Which of the following shows a good example of Step 4? 4. Follow the flow of the short line segments to sketch a function y (t). Our y (t) sketch must never cross a tangent line, and it should have slopes that are aligned with the tangent line segments.

This is the idea of a slope field graph: 1. Our goal is to sketch the unknown function y (t). 2. We are given a differential equation that allows us to calculate slope values of y (t). 3. We sketch short line segments that have the correct slopes at many points in the plane. These are tangent lines. 4. Follow the flow of the short line segments to sketch a function y (t). Our y (t) sketch must never cross a tangent line, and it should have slopes that are aligned with the tangent line segments. Consider the differential equation y' = y+¤ ·e¯² +1. Steps 1, 2, and 3 have been completed and the result is shown here: Which of the following shows a good example of Step 4? 4. Follow the flow of the short line segments to sketch a function y (t). Our y (t) sketch must never cross a tangent line, and it should have slopes that are aligned with the tangent line segments.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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