To find: If
Answer to Problem 8RWDT
It is not necessary to follow that the corresponding polar curve is the graph of
Explanation of Solution
Given information:
The polar curve
In the Cartesian
In the cartecian coordinate sysytem the equation of the function is represented as
If in polar coordinate system curve
Let take an example
By the definition of continuity for functions of a single variable a function
For every
If the function is single variable the statement is true but if the function is multivariable then the statement is not always true.
In order to shoe that let take an example:
If this limit is converted into polar coordinates, it becomes
Like substitute
The limit exists but if the path is change it is not necessary that the limit exists. For a function being continuous the limit should exists following every path.
With polar coordinates it is just "parametrizing" all the point in the neighborhood of
Therefore if
Chapter 10 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
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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