📝 题目
5. 5.1 求下列极限:}
(1) $\displaystyle{\mathop{\lim }\limits_{{x \rightarrow 0}}{\int }_{-1}^{1}\sqrt{{x}^{2} + {y}^{2}}\mathrm{\;d}y}$ ; (2) $\displaystyle{\mathop{\lim }\limits_{{x \rightarrow 0}}{\int }_{0}^{2}{y}^{2}\cos {xy}\mathrm{\;d}y}$ ; (3) $\displaystyle{\mathop{\lim }\limits_{{a \rightarrow 0}}{\int }_{a}^{1 + a}\frac{\mathrm{d}x}{1 + {x}^{2} + {a}^{2}}}$ .
💡 答案与解析
5. 5.1 (1) $1;\;\left( 2\right) \frac{8}{3};\;\left( 3\right) \frac{\pi }{4}$ .