x趋向于无穷时,ax+b-(2x^2-1)/(x-1)的极限为1,求常数a,b.
问题描述:
x趋向于无穷时,ax+b-(2x^2-1)/(x-1)的极限为1,求常数a,b.
算出了a=2,b算不出来
答
lim【x→∞】ax+b-(2x²-1)/(x-1)=lim【x→∞】[(ax+b)(x-1)-(2x²-1)]/(x-1)=lim【x→∞】[(a-2)x²+(b-a)x+1-b]/(x-1)=lim【x→∞】[(a-2)x+(b-a)+(1-b)/x]/(1-1/x)因为极限是1所以a-2=0b-a=1解得a=2b...