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计算下列极限:
(1) $\lim _{x \rightarrow+\infty} \frac{\int_1^x\left[t^2\left(\mathrm{e}^{\frac{1}{t}}-1\right)-t\right] \mathrm{d} t}{x^2 \ln \left(1+\frac{1}{x}\right)}$.
(2) $\lim _{x \rightarrow+\infty}\left(x+\sqrt{1+x^2}\right)^{\frac{1}{x}}$.
                        
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