当xx-1/2x^2

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当xx-1/2x^2当xx-1/2x^2当xx-1/2x^2（注,原题有误,应为＜号）令f(x)=ln(1+x)-x+(1/2)x^2求得f''(x)=(x^2)/(1+x)显然,f(x)的定义域为(-

当xx-1/2x^2
当xx-1/2x^2

当xx-1/2x^2
（注,原题有误,应为＜号）
令 f(x)=ln(1+x)-x+(1/2)x^2
求得
f'(x)=(x^2)/(1+x)
显然,f(x)的定义域为(-1,+无穷),即在其定义域内,有
f'(x)≥0
又
f(0)=0
而在区间(-1,0)
f'(x)＞0
故必有
f(x)-f(0)＜0
即
f(x)＜f(0)=0
即
ln(1+x)-x+(1/2)x^2＜0
即
ln(1+x)＜x+(1/2)x^2

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