若lim(x-0)[(x^2/x+1)-ax-b]=0,求常数a,b
问题描述:
若lim(x-0)[(x^2/x+1)-ax-b]=0,求常数a,b
应该是lim(x-无穷),打错了
答
lim(x-∞)[(x^2/x+1)-ax-b]=lim(x-∞)[(x^2 -1+1)/x+1)-ax-b]=lim(x-∞)[x -1+ 1/(x+1)-ax-b]=lim(x-∞)[(1-a)x -(1+b)+ 1/(x+1)]=lim(x-∞)[(1-a)x -(1+b)]若此极限=0,那么只能有 1-a=0 且 1+b=0a=1 b= -1...