Question

f(x)=(x+1)2+xsinx除以x2+1

Answer 1

f(x)=[(x+1)²+sinx]/(x²+1)

=(x²+1+2x+sinx)/(x²+1)

=1+(2x+sinx)/(x²+1)

设g(x)=(2x+sinx)/(x²+1),即g(x)=f(x)-1

则容易知道g(x)的奇函数,

且 g(x)的最大值为M-1,g(x)的最小值为m-1

∴ (M-1)+(m-1)=0

∴ M+m=2