Well, I mean, imagine that you have a function: $f(x)=\lim\limits_{x\to n}{\dfrac{nx}{x^n}}$ Would it be possible to write an integral of that? Something like this: $\int{\biggl(\lim_{x\to n}\dfrac{nx}{x^n}\biggl)}dx$
Limit inside an integral
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calculus
integration
limits
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0we will calculate the integral of a constant. – 2012-04-27
2 Answers
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yes, you can do it but if $\lim\limits_{n\to +\infty}f_{n}(x)=f(x)\in L^1$
$\int \lim_{n\to +\infty}f_{n}(x)dx=\int f(x)dx$
0
Of course you can do it,
$\displaystyle\int{\biggl(\lim\limits_{x\to n}\dfrac{nx}{x^n}\biggl)}dx= \displaystyle\int L.dx = Lx +c $
$L= n^{2-n}$
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0@Garmen1778 yes L(limit) is $n^{2-n}$ – 2012-04-28