General Implicit Function/Examples
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Examples of General Implicit Functions
Example: $u^2 + x^2 + y^2 = a^2$
Consider the equation:
- $(1): \quad u^2 + x^2 + y^2 = a^2$
where $u, x, y \in \R$ are real variables.
Then $(1)$ defines $u$ as an implicit function of $x$ and $y$ on the region $x^2 + y^2 \le a^2$.