高等数学判断奇偶性？ 高等数学函数的奇偶性判断
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1.f(-x)=f(x)\uff0c\u662f\u5076\u51fd\u6570
2.f(-x)+f(x)=0\uff0c\u662f\u5947\u51fd\u6570
\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.
判断函数y(x)的奇偶性，先看定义域是否关于原点对称，然后计算y(-x)的值，看是否等于-y(x)(此时y(x)为奇函数)或y(x)(此时y(x)为偶函数)。
该函数的定义域为实数，故定义域关于原点对称。可以验证y(-x)=-y(x)。故该函数为奇函数。
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