试将函数[tex=6.429x2.786]KxH31rE037r1nCSwh+zvwDWZtD0vGCZcTP5ojFn1RXTeEMgTG7/cDYJn2GGp5OK5[/tex]展为麦克劳林级数,并写出其收敛域.

求下列曲线在坐标平面[tex=1.857x1.214]TDhC/aEJZhH/Z63BLwHl0A==[/tex]上的投影曲线方程：[tex=6.429x2.786]7EJHVCtO2IWq3KpdB+jQsizWA8nFAfzXF+Xk1Tz6JRMzyFnq1i3N9Go1m+Aj1SCyJnEqU90mwt7UojgVo9BKHQ==[/tex]

已知一抛物线[tex=5.714x2.786]L6t4fJbqVB11cvmaLyp++OHfiyxHhNonplnwzD/p6TPeIrsipvCrtfH0iwyWYyh/dPmYkt1TAT+ztHzNJCWQ/Zd40vm17ArLdVWjwILNduk=[/tex]平行移动，且顶点总在抛物线[tex=6.429x2.786]3X4AXgzEacl6vAVPBBrqw5eMaplK588BpFuJKxY26o6O/wj6KH46oLjjAO4moA1gWtrS1Hwc6qtamJk9g3SrHplIrizTZ765ipuw2Ne84h0=[/tex]上，试求其轨迹方程.

当 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex]为何值时，反常积分[tex=6.429x2.786]PJkWCDHq0HBl1uIZQZIQaAQKDrmXbAa2BP9X+F9KcEXbmbpBFRWCul9iGn0Yld/C[/tex] 收敛? 又当[tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 为何值时，该反常积分发散?

设已给出[tex=8.0x1.429]9GyxgdHDghAOvXbZiQljfHUXk3G+1ZKYX1RLCw+U1z8=[/tex]的数据表，分别用复化梯形法与复化辛普生法求积分[tex=6.429x2.786]u5/riQTd+DtIC9kBnmlD4JHlSkd7vt+1bsR21G/hXbA=[/tex]的近似值。[img=1031x86]178212db424a6e0.png[/img]

设[tex=4.429x1.214]W1uTpzbbehOOliAP2ns4cw==[/tex] 都是[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex] 阶方阵，[tex=8.929x1.214]1FNc07kDow5egXRYL8+GLIk7vDMrbYttx818/g+jV6q6QtJ9Gh6nv1VcLLQ/dBbjNchFbeZsyfahzs7UlvpmUrQ4prQbVDwkBK0ZUgOjgw0=[/tex]，且[tex=3.143x1.357]jmW/UUDE3QEpfgsRbhrpUQ==[/tex]，若[tex=6.429x2.786]PIak5GQdBqGUzEAptxxv/Z8SaMnYrAfVK2xH70RinvoRAo9mJps9nCyiEGu0xfuhSM0KJ5kNq/GK7j9LCYCwzg==[/tex]，求证：[tex=6.714x1.357]Eg85/bKr5EFuE5mFPEmoaSu70vGsYdU89+dKRhtbDUs=[/tex]

下列变量组（）是一个闭回路。 A: {x，x，x，x，x，x} B: {x，x，x，x，x} C: {x，x，x，x，x，x} D: {x，x，x，x，x，x}

以下谓词蕴含式正确的是（）: (∀x) (A(x)→B(x))=>( ∀x)A(x)→(∀x)B(x)|(∀x) (A(x)↔B(x))=>( ∀x)A(x)↔(∀x)B(x)|(∀x)A(x)∨(∀x)B(x)=>( ∀x) (A(x)∨B(x))|(∃x) (A(x)∧B(x))=>(∃x)A(x)∧(∃x)B(x)

以下谓词蕴含式正确的是（）: (?x) (A(x)→B(x))=>( ?x)A(x)→(?x)B(x)|(?x) (A(x)?B(x))=>( ?x)A(x)?(?x)B(x)|(?x)A(x)∨(?x)B(x)=>( ?x) (A(x)∨B(x))|(?x) (A(x)∧B(x))=>(?x)A(x)∧(?x)B(x)

下列式中错误的是： A: (∀x)(A(x)Úp(x)) Û (∀x)A(x)Ú (∀x)p(x) B: ($x)A(x) Ù p Û ($x)(A(x) Ù p ) C: (∀x)(A(x)ÚB(x)) Þ (∀x)A(x)Ú( ∀x)B(x) D: ($x)(A(x)ÙB(x)) Þ ($x)A(x)Ù( $x)B(x)