query: consider a function $(x,y)$ given by...
positive_passages.docid: 109994
positive_passages.text: Show discontinuity of $\frac{xy}{x^2+y^2}$
negative_passages.docid: 78753
negative_passages.text: $f(x,y)=4x^3y^2$ Dealing with Directional Derivatives and Vectors
negative_passages.docid: 28286
negative_passages.text: About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
negative_passages.docid: 71049
negative_passages.text: Functional equation $f(xy)=f(x)+f(y)$ and continuity
negative_passages.docid: 127338
negative_passages.text: Intuitive characterization of the graph of a twice differentiable function
negative_passages.docid: 149390
negative_passages.text: Fixed point of a Function (monotonically increasing)
negative_passages.docid: 73073
negative_passages.text: Differentiating $y=x^{2}$
negative_passages.docid: 11806
negative_passages.text: Functional equation.
negative_passages.docid: 40121
negative_passages.text: Asymptotes of function
negative_passages.docid: 148470
negative_passages.text: bound of the function
negative_passages.docid: 98363
negative_passages.text: Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
negative_passages.docid: 79281
negative_passages.text: Let $f : X \to Y$ be a function and $E \subseteq X$ and $F \subseteq X$. Show that in general
negative_passages.docid: 124861
negative_passages.text: The extension of smooth function
negative_passages.docid: 137043
negative_passages.text: To show that function is constant
negative_passages.docid: 141423
negative_passages.text: The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
negative_passages.docid: 37976
negative_passages.text: Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$