高数中函数的奇偶性问题 高中数学函数的奇偶性问题
\u9ad8\u7b49\u6570\u5b66\u51fd\u6570\u7684\u5947\u5076\u6027\u5224\u65ad\uff081\uff09.e^\uff08-1/x2\uff09\u662f\u5076\u51fd\u6570,x\u662f\u5947\u51fd\u6570,\u6240\u4ee5xe^\uff08-1/x2\uff09\u662f\u5947\u51fd\u6570,\u800carctanx\u4e5f\u662f\u5947\u51fd\u6570,\u6240\u4ee5f\uff08x\uff09=xe^\uff08-1/x2\uff09 +arctanx\u662f\u5947\u51fd\u6570\uff1b\uff082\uff09.xsinx\u662f\u5076\u51fd\u6570,1+x2\u4e5f\u662f\u5076\u51fd\u6570,\u6240\u4ee5f\uff08x\uff09=\uff08xsinx\uff09/\uff081+x2\uff09\u4e5f\u662f\u5076\u51fd\u6570\uff1b\uff083\uff09.f\uff08x\uff09=(e^x-1)/(e^x+1)=1-2/\uff08e^x+1\uff09,f\uff08-x\uff09=1-\uff082e^x\uff09/\uff08e^x+1\uff09,\u800cf\uff08-x\uff09+f\uff08x\uff09=0\u53ef\u77e5f\uff08x\uff09= - f\uff08-x\uff09,\u6240\u4ee5f\uff08x\uff09\u4e3a\u5947\u51fd\u6570.
\u4e0a\u9762\u7684\u8bf4\u9519\u4e86\uff0c\u662f\u540e\u8005\uff0c\u6211\u4ee5\u9ad8\u4e2d\u6570\u5b66\u66fe\u7ecf\u83b7\u5f97\u6ee1\u5206\u7684\u540d\u8a89\u62c5\u4fdd\u3002\u5176\u5b9e\u6211\u4eec\u53ef\u4ee5\u8bbeg\uff08x\uff09=f\uff08x+2)\uff0c\u90a3\u4e48\u56e0\u4e3af\uff08x+2\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u5219g\uff08x\uff09\u4e5f\u4e3a\u5076\u51fd\u6570\uff0c\u5373 g\uff08-x\uff09=g\uff08x\uff09\u3002\u90a3\u4e48\u4e5f\u5c31\u662ff\uff08-x+2\uff09=f\uff08x+2\uff09\u3002\u3002\u3002\u3002\u603b\u4e4b\u8bf4f\uff08x+2\uff09\u662f\u5076\u51fd\u6570\uff0c\u90a3\u4e48\u8bf4\u7684\u5c31\u662fx\uff0c\u4ee5\u4e3a\u90a3\u4e2a\u51fd\u6570\u7684\u53d8\u91cf\u5c31\u662fx\uff0c
f(-x)=-f(x)即为奇函数。
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绛旓細f(-x)=-f(x)鍗充负濂鍑芥暟銆
绛旓細瑙ｅ涓嬪浘鎵绀
