• 2022-11-01
    设上半平面[tex=9.0x1.286]zGvY4AigE1CGoWcuhr0/Qv16ugzGw/p5BlzCdKlWnOI=[/tex]内函数[tex=3.357x1.286]wErsnHRY9kGFNaB4WcQbMw==[/tex]具有连续偏导数,且对任意的[tex=2.143x1.286]A2agUMZvwLAtUDCRr2pc9A==[/tex], 都有[tex=10.071x1.286]gEXIPBMqSFgoCq9ZL3MD7jyRrPgBvlFGVKLrcyv0ikOQPJot2JYzRFmI5SvBDZxB[/tex]。 证明: 对[tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex]内任意分段光滑的有向简单闭曲线[tex=0.714x1.286]LA74ioWWkXdGbHCtFk/Sog==[/tex]都有[tex=14.143x2.214]SKMsDyFW+XJmqTZRIKpCL1CX/Blgw4Zv2N1QXwkAJWVxv+2fZk89gTDhquFKVj+3R3icEdjUigUqzlLxmF5zlw==[/tex]。
  • 分析 证明对[tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex]内任意分段光滑的有向简单闭曲线[tex=0.714x1.286]LA74ioWWkXdGbHCtFk/Sog==[/tex]上的曲线积分为零,可考虑利用其充分条件:在单连通域内[tex=4.357x2.214]V9fVXReHUrcmKJSTnoNlS+m+sqsVguAfUlcXLQaFRyR18eA/4il18f2isWJ4UAAhhSB1bNfH9nO+6DjjQrlTZI79k0YSM/hMz+uaw69EjEQ=[/tex]。试 在所给曲线积分[tex=12.357x2.214]SKMsDyFW+XJmqTZRIKpCL+Qa1siQFCTmAmvqdTHkKP0q7bPXqwXXijflQWIX1u3R[/tex] 中,[tex=5.929x1.286]WfCD2Tb6lXob4iH5/FTPzKbK41adbNTu3FaOpwoaxcA=[/tex],[tex=6.714x1.286]naOBvVLoICuxXy8FuYU8COLiWuKwvUvdxQXRjv0mZUI=[/tex],[tex=11.643x2.214]V9fVXReHUrcmKJSTnoNlS1KS/fQXa8GdYgRXmH87+AwnkzCjpkPRV5T6O7Y7HwBHBmBeFYAA6UJF4xJKHnWmmvRL4iAI7QTwFuD5zyOSMgs=[/tex],(*)[tex=12.429x2.071]V9fVXReHUrcmKJSTnoNlS+m+sqsVguAfUlcXLQaFRyTu7vdvBSyfH5tgnERJ4ogjgvGx7igAxFOVtor6UTy0phbuEh/56EC2vHiM36y2mWM=[/tex],将[tex=10.071x1.286]gEXIPBMqSFgoCq9ZL3MD7jyRrPgBvlFGVKLrcyv0ikOQPJot2JYzRFmI5SvBDZxB[/tex]两端关于[tex=0.357x1.286]tv9NEQGfxmSBsvmqN3/Q7Q==[/tex] 求导数,可得[tex=8.571x1.286]iqKxeUqBVaQsagV9iAPmtw4iBIc3ww6KGGHOp3nugvW80rpx0umLnkyvnDo1+FAcLvEfBvP6g0e3tHTqlwPY9w==[/tex]。因此令[tex=2.143x1.286]tB3xY19iQ1U20WlOQhphvg==[/tex]可得[tex=15.571x1.357]0tcDT7WoJIjUe8H8auMPykbVxxCfj4zw6uyEPHxxZrX00e0evabUFQhN4p0fafqh0o7Ki04r2E9oFRZVVRh7AKDt8De4wzBugH+QwS8hmws=[/tex]代入(*)可得[tex=15.214x5.5]SMCiZCjCLMG8LLJWa9iOzONMWo3nC7LQmY4lIhU6uuJZF4rvYblfHX2yIWsGT+iJK0n/J44Kvi5S/PbJcVkewW+wz7V/b+ymASo44sHJdNUc5SZXB+1QNmgsspgRy/4bqgWn22zznP6AiXdA/Lp1NGZi1xlgnVX/Xcp+lEp2HGeInjw8N4ikqaxnyTNdtX9uDKJr+wjgVx14RFeYwxN1zz/tsFiKnFchLPQpCwmwgw1fNyyUUKjUXYrVNlzMz9XE[/tex]可知当[tex=2.143x1.286]A2agUMZvwLAtUDCRr2pc9A==[/tex]时,对[tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex]内任意分段光滑的有向简单闭曲线[tex=0.714x1.286]LA74ioWWkXdGbHCtFk/Sog==[/tex] 都有[tex=14.143x2.214]SKMsDyFW+XJmqTZRIKpCL+Qa1siQFCTmAmvqdTHkKP1qby/bgK2gBJhN47MeZBL3nP4J79a/RuB9Ad4pJ/w8xg==[/tex]。
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    举一反三

    内容

    • 0

      [tex=2.214x1.0]Z8GWW72u+MH/mjafnp+83A==[/tex]丙酮酸经过丙酮酸脱氢酶系和柠檬酸循环产生[tex=4.0x1.214]EPDWVFNjIR8daNoozaWRDg==[/tex],生成的[tex=3.214x1.0]1AqDCKqjaAug6buHS5Z0tQ==[/tex]、[tex=3.429x1.214]HYAn2+I9AZQLWcA3ajoPaw==[/tex]和[tex=2.143x1.0]qQANfGnLx7pE5mcaEibuNg==[/tex](或[tex=2.071x1.0]YGdeb/NAM7yg+XY6SY16Fg==[/tex])的摩尔比是(  )。 未知类型:{'options': ['3:2:0', '4:2:1', '4:1:1', '3:1:1', '2: 2:2'], 'type': 102}

    • 1

      设h为X上的函数,证明下列两个条件等价。(1)h为一满射,(2)对任意X上的函数[tex=5.429x1.214]OREhy0bsXZWZ6y8PdI7nwHYlaKprN6KYnR/FCpmEbdk=[/tex]蕴涵[tex=1.786x1.214]pxzkG5OdsKT9CiCwC5OvPQ==[/tex]

    • 2

      设常数[tex=2.357x1.286]a9xCMucObW1FOUJSgznh5w==[/tex],函数[tex=2.929x1.286]bxDJBD1eh7UoKfKs5gMhsA==[/tex][tex=5.214x1.786]GRPxR1BEEgqTAA3YSC0aDhWRX6RY9Wq2eVhU0y8/0sA=[/tex]在[tex=3.357x1.286]U+f1Q3HlF52kntNzvjvu1pY0SaSCwNNc7bZDyBONdew=[/tex]内零点个数为 A: 3 B: 2 C: 1 D: 0

    • 3

      设[tex=5.214x1.214]l2vYijvwphpA0Bdo8olvNhKvOVd4RCELKut0jj6S5qs=[/tex]是连续映射,Y是Hausdorff空间,证明:(1)集合[tex=9.357x1.357]QCqopxinhs+TvVYgLw48vVpO4x/Rie4gzAlmw62rJGM=[/tex]是X的闭子集;(2)如果A是X的稠密子集且[tex=3.714x1.357]fo4X83uQk0aLKgSpBjpSMw8oj58YdJ5bCiu5d4gfWQqZvgjwV7CYEcyqXJHmRmoq[/tex],则f=g。

    • 4

      已知[tex=10.786x1.357]oPxEQGciaJq0uWonaJqXssvTKx2aAMqoshLd51U2O4M=[/tex],若[tex=2.0x1.214]IENxQEh5u4RdnCaqHm72Xg==[/tex]相互独立,则[tex=3.0x1.357]cl60lRnHnAb2Fyha9FYNvw==[/tex] A: 1/2 B: 1/3 C: 2/3 D: 3/4