Real Function of Two Variables/Substitution for y/Examples/x + y/1 over 2
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Examples of Substitution for $y$ in Real Function of Two Variables
Let $\map f {x, y}$ be the real function of $2$ variables defined on the domain $S \times T$ as:
- $\forall \tuple {x, y} \in S \times T: \map f {x, y} := x + y$
where $S$ and $T$ are the closed real intervals:
\(\ds S\) | \(:=\) | \(\ds \closedint {-1} 1\) | ||||||||||||
\(\ds T\) | \(:=\) | \(\ds \closedint 0 2\) |
Let $\dfrac 1 2$ be substituted for $y$ in $\map f {x, y}$.
Then:
\(\ds \forall x \in \closedint {-1} 1: \, \) | \(\ds \map f {x, \dfrac 1 2}\) | \(=\) | \(\ds x + \dfrac 1 2\) |
Sources
- 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text C$: Function of Two Independent Variables: Example $2.67 \ \text {(a)}$