高数，奇偶性判断 高数，判断奇偶性
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y=x是奇函数，主要看y=ln(x+√(x²+1))是奇函数还是偶函数，
f(-x)=ln(-x+√(x²+1))=ln[(-x-√(x²+1))/(x²-x²-1)]=ln(x+√(x²+1))=f(x)
即y=ln(x+√(1+x²))是偶函数
所以
y=xln[x+√(x²+1)]是奇函数
用定义即可
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绛旓細1-e^-(-x),-x鈮0 锛-x鈮0 锛屽垯x>0)f(-x)={ e^锛-x锛-1,-x锛0 (-x>0,鍒檟 鎵浠ュ氨鍙寲涓 1-e^(x),x鈮0 f(-x)={ e^锛-x锛-1,x锛0 鍐欐硶涓婁笅鎹綅缃紝涓旀彁鍙栦竴涓礋鍙枫傚嵆 e^(x)-1 ,x锛0 f(-x)= -{ 1-e^锛-x锛,x鈮0 =-f(x锛夋墍浠ユ槸濂囧嚱鏁般傦紙娉ㄥ仛棰...
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绛旓細褰 a=0锛宖(u) 涓洪潪濂囬潪鍋跺嚱鏁版椂锛屸埆<0,y>dx鈭<0,x>xf(u)du 鏄潪濂囬潪鍋跺嚱鏁般傚綋 a鈮0 鏃讹紝鈭玠x鈭玿f(u)du 涓鑸槸闈炲闈炲伓鍑芥暟銆備緥濡 鈭<1,y>dx鈭<1,x>2xudu = 鈭<1,y>xdx鈭<1,x>2udu = 鈭<1,y>x(x^2-1)dx = [x^4/4-x^2/2]<1,y> = y^4/4-y^2/2...
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