Suppose f(x,y) is some continuous, smooth function with the property(adsbygoogle = window.adsbygoogle || []).push({});

[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

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# [Question] Limit and Integration

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