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Suppose f(x,y) is some continuous, smooth function with the property
[tex]\lim_{y \to 0}f(x,y)=1
[/tex]
and g(x) is some other continuous smooth function.
I want to know if this is true:
[tex]
\lim_{y \to 0} \int_{a}^{b}g(x)f(x,y)dx =? \int_{a}^{b}g(x)dx[/tex]
How can I show that it is or isn't true? For which case will it be true or not true?
Thanks
[tex]\lim_{y \to 0}f(x,y)=1
[/tex]
and g(x) is some other continuous smooth function.
I want to know if this is true:
[tex]
\lim_{y \to 0} \int_{a}^{b}g(x)f(x,y)dx =? \int_{a}^{b}g(x)dx[/tex]
How can I show that it is or isn't true? For which case will it be true or not true?
Thanks