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Calculer : \[\lim\limits_{a\rightarrow 0^{+}}\int_{a}^{3a}\frac{\tan t}{t^{2}}dt \ ,\ \lim\limits_{n\rightarrow \infty }\int_{0}^{1}\frac{x^{n}-x^{2n}}{1-x}dx.\]
Calculer : \[\lim\limits_{a\rightarrow 0^{+}}\int_{a}^{3a}\frac{\tan t}{t^{2}}dt \ ,\ \lim\limits_{n\rightarrow \infty }\int_{0}^{1}\frac{x^{n}-x^{2n}}{1-x}dx.\]