Other Math Archive: Questions from November 02, 2022
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Exercise 2 Compute the gradient of the functions (a) \( f(x, y)=\sin \left(x^{2}+y^{2}\right) \). (b) \( g(x, y)=\frac{1}{x^{2}+y^{2}} \). (c) \( h(x, y, z)=\frac{x}{1+y^{2}}-z \).2 answers -
Let \( R(x, y) \) be a binary relation on \( D \). \( R \) is NOT symmetric if: a. \( \forall x . \forall y \cdot[R(x, y) \rightarrow R(y, x)] \) b. \( \forall x . \forall y .[(R(x, y) \wedge R(y, x))2 answers -
\( \forall x . \forall y \cdot[R(x, y) \rightarrow R(y, x)] \) \( \forall x . \forall y \cdot[(R(x, y) \wedge R(y, x)) \rightarrow(x=y)] \) \( \exists x . \exists y .[R(x, y) \rightarrow R(y, x)] \) b2 answers -
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ze \( c=3 x+y+5 z \) subjes \[ \begin{array}{l} x+y+z \geq 80 \\ 2 x+y \geq 60 \\ y+z \geq 60 \\ x \geq 0, y \geq 0, z \geq 0 \end{array} \] \[ c= \]2 answers