Chapter 3: Functions of Several Variables
Section 3.2: Limits and Continuity
Example 3.2.24
Extend to a function that is continuous at the origin.
Solution
The requisite extension assigns to the origin the value of the bivariate limit of at the origin. Hence, what is required is to show that this limit is zero, a computation summarized below.
Inequality 5
Table 3.2.1
Inequality 6
Since , it is clear that as . Hence, the required extension is
Indeed, = .
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