比较二重积分的大小? 比较二重积分的大小,谢谢。
\u6bd4\u8f83\u4e8c\u91cd\u79ef\u5206\u7684\u5927\u5c0f\u6211\u89c9\u5f97\u4f60\u662f\u5bf9\u53cc\u91cd\u79ef\u5206\u7684\u5b9a\u4e49\u7406\u89e3\u51fa\u4e86\u95ee\u9898\uff0c\u8001\u5e08\u4e0a\u8bfe\u65f6\u7684\u5b9a\u4e49\u516c\u5f0f\u63a8\u5bfc\u4f30\u8ba1\u4f60\u6ca1\u8ba4\u771f\u542c\u5566\u3002\u53cc\u91cd\u79ef\u5206\u7684\u503c\u53ef\u4ee5\u7528\u7269\u7406\u4e2d\u7684\u4f53\u79ef\u6765\u7c7b\u6bd4\u3002\u5728\u4e09\u7ef4\u76f4\u89d2\u5750\u6807\u7cfbx\u3001y\u3001z\u4e2d\uff0c\u4ee4z = f(x,y) = x + y\uff0c\u5219 1. \u79ef\u5206\u533a\u57dfD\u662f\u51fd\u6570z = f(x,y)\u5728x\u3001y\u5e73\u9762\u7684\u6295\u5f71\uff08\u7b80\u5355\u7684\u8bf4\uff0c\u79ef\u5206\u533a\u57df\u5c31\u76f8\u5f53\u4e8e\u201c\u5e95\u9762\u79ef\u201d\uff09\uff1b 2. \u88ab\u79ef\u51fd\u6570z = f(x,y)\u5c31\u76f8\u5f53\u4e8e\u201c\u9ad8\u201d\uff1b 3. \u53cc\u91cd\u79ef\u5206\u7684\u503c\u5c31\u76f8\u5f53\u4e8e\u201c\u4f53\u79ef\u201d\u3002\u6240\u4ee5\uff0c\u5728\u76f8\u540c\u7684\u533a\u57dfD\u5185\uff0cz = f(x,y)\u7684\u503c\u8d8a\u5927\uff0c\u90a3\u4e48\u53cc\u91cd\u79ef\u5206\u7684\u503c\u4e5f\u5c31\u8d8a\u5927\u3002
\u8fd9\u4e2a\u95ee\u9898\uff0c\u5e94\u8be5\u662f\u6d89\u53ca\u5230\u6c42\u4f53\u79ef\u7684\u65f6\u5019\u5427\uff0c\u5176\u5b9e\u4e8c\u91cd\u79ef\u5206\u8ddf\u4e09\u91cd\u79ef\u5206\u90fd\u53ef\u4ee5\u6c42\u4f53\u79ef
\u88ab\u79ef\u51fd\u6570\u4e3a1\u7684\u4e09\u91cd\u79ef\u5206\uff0c\u8868\u793a\u79ef\u5206\u533a\u57df\u7684\u4f53\u79ef
\u4e8c\u91cd\u79ef\u5206\u8868\u793a\u66f2\u9876\u67f1\u4f53\u7684\u4f53\u79ef
所以 ln(x²+y²+1)≤ln(x+y+1),
前大,后小。
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