\(\lim \limits_{(x,y) \to (2,2)} { { x + y} \over {xy}} = \)______
举一反三
- \(\lim \limits_{(x,y) \to (2,0)} { { \tan xy} \over y} = \)______
- 下列函数中，( )不是方程\( xy' + y - x^2 = 0 \)的解。 A: \( y = { { {x^2}} \over 3} + {1 \over x} \) B: \( y = { { {x^2}} \over 3} \) C: \( y = { { {x^2}} \over 3} + 2 \) D: \( y = { { {x^2}} \over 3} - {1 \over x} \)
- \( \lim \limits_{x \to 0} {x^2}\sin {1 \over x} =\)______。______
- 将\(f(x) = {1 \over {2 - x}}\)展开成\(x \)的幂级数为（ ）。 A: \({1 \over {2 - x}} = \sum\limits_{n = 0}^\infty { { { { x^n}} \over { { 2^{n }}}}} \)，\(( - 2,2)\) B: \({1 \over {2 - x}} = \sum\limits_{n = 0}^\infty { { { { x^n}} \over { { 2^{n }}}}} \)，\(\left( { - 2,2} \right]\) C: \({1 \over {2 - x}} = \sum\limits_{n = 0}^\infty { { { { x^n}} \over { { 2^{n + 1}}}}} \)，\(( - 2,2)\) D: \({1 \over {2 - x}} = \sum\limits_{n = 0}^\infty { { { { x^n}} \over { { 2^{n + 1}}}}} \)，\(\left( { - 2,2} \right]\)
- \( \lim \limits_{x \to 0} { { \sqrt {1 + x\sin x} - \cos x} \over { { {\sin }^2}{x \over 2}}} = \)______ 。