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I need help to prove this.

Let $f:\mathbb{R}\longrightarrow{\mathbb{R}}$ be an absolutely continuous function in any interval of the form $\left. [ -k,k \right ]$. If $f^{\prime}$ is in $L(\mathbb{R})$ and $\left\{{x_n}\right\}$ is a sequence that converges to infinity. Show that $\displaystyle\lim_{n \to{\infty}}{\displaystyle \left |{f(1+x_n)-f(x_n)}\right |}=0$


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closed as off-topic by 6005, Davide Giraudo, Shuchang, hardmath, AlexR Dec 13 '13 at 14:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – 6005, Davide Giraudo, Shuchang, hardmath, AlexR
If this question can be reworded to fit the rules in the help center, please edit the question.

If $f$ is absolutely continuous $[a,b]$, then f has a derivative $f′$ almost everywhere, the derivative is Lebesgue integrable, and $f(x) = f(a) + \int_a^x f'(t) \, dt$. – Mhenni Benghorbal Dec 13 '13 at 9:30
What is the role in your hint of the form $\left. [ -k,k \right ]$ of the intervals? – user95747 Dec 13 '13 at 10:33

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