Concept explainers
To draw : the direction field using computer algebra system and sketch on it the solution curve that passes through the point.
Explanation of Solution
Given information :
The differential equation is
Graph :
By using computer algebra system,
The direction field is obtained as:
To sketch the solution curves first sketch the solution, for sketching solution start at the origin and move to the right in the direction of the line segment (which has slope 1), then continue the solution curve so that it moves parallel to the nearby line segments. And for more solution curve change the y -intercept.
Since solution graph passes through the point
For various value of c solution will be different,
So the graph can be observed as:
To find the value where the limit exist,
Because in the solution of the differential equation, log does not take negative and zero value, so limit will be exist if the value of
The value of limit is always
Interpretation : from the above graph it can be observed that Because in the solution of the differential equation, log does not take negative and zero value, so limit will be exist if the value of
The value of limit is always
Chapter 7 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning