📝 题目
5.1.14 求下列函数的极限:
(1) $\mathop{\lim }\limits_{{\left( {x,y}\right) \rightarrow \left( {0,0}\right) }}\frac{{\mathrm{e}}^{x} + {\mathrm{e}}^{y}}{\cos x + \sin y}$ ; (2) $\mathop{\lim }\limits_{{\left( {x,y}\right) \rightarrow \left( {0,0}\right) }}\frac{{x}^{2}{y}^{3/2}}{{x}^{4} + {y}^{2}}$ ;
(3) $\mathop{\lim }\limits_{\substack{{x \rightarrow + \infty } \\ {y \rightarrow + \infty } }}\left( {{x}^{2} + {y}^{2}}\right) {\mathrm{e}}^{-\left( {x + y}\right) }$ ; (4) $\mathop{\lim }\limits_{{\left( {x,y}\right) \rightarrow \left( {0,0}\right) }}\frac{\sin \left( {{x}^{3} + {y}^{3}}\right) }{{x}^{2} + {y}^{2}}$ .
💡 答案与解析
5.1.14 (1) 2; (2) 0; (3) 0; (4)