- #1
jostpuur
- 2,116
- 19
Can you give an example of a function [itex]f:X\times Y\to\mathbb{R}[/itex], where [itex]X,Y\subset\mathbb{R}[/itex], such that the integral
[tex]
\int\limits_Y f(x,y) dy
[/tex]
converges for all [itex]x\in X[/itex], the partial derivative
[tex]
\partial_x f(x,y)
[/tex]
exists for all [itex](x,y)\in X\times Y[/itex], and the integral
[tex]
\int\limits_Y \partial_x f(x,y) dy
[/tex]
diverges at least for some [itex]x\in X[/itex]?
[tex]
\int\limits_Y f(x,y) dy
[/tex]
converges for all [itex]x\in X[/itex], the partial derivative
[tex]
\partial_x f(x,y)
[/tex]
exists for all [itex](x,y)\in X\times Y[/itex], and the integral
[tex]
\int\limits_Y \partial_x f(x,y) dy
[/tex]
diverges at least for some [itex]x\in X[/itex]?