\( \lim \limits_{x \to {0^ + }} {\left( {\cot x} \right)^ { { 1 \over {\ln x}}}} \)=_____ ______
举一反三
- 下列极限计算正确的是( ). A: \(\lim \limits_{x \to 0} { { \left| x \right|} \over x} = 1\) B: \(\lim \limits_{x \to {0^ + }} { { \left| x \right|} \over x} = 1\) C: \(\lim \limits_{x \to 0} {(1 - {1 \over {2x}})^{2x}} = {e^{ - 1}}\) D: \(\lim \limits_{x \to \infty } {(1 - {1 \over {2x}})^{2x}} = e\)
- 求极限\( \lim \limits_{x \to {0^{\rm{ + }}}} {\left( {\cot x} \right)^{\sin x}}{\rm{ = }}\)__________
- \( \mathop {\lim }\limits_{x \to 0} { { \left( { { e^x} - 1} \right)\sin 2x} \over {1 - \cos x}} = \)______ 。
- \(\lim \limits_{x \to 1} { { \sin \left( { { x^2} - 1} \right)} \over {x - 1}}{\rm{ = }}\)______ 。
- \( \lim \limits_{x \to {0^ + }} { { \ln \sin 3x} \over {\ln \sin x}} = 3 \)。