设a,b为常数,(ax²/(x+1))+bx当x趋于0时极限等于2,则a+b=?

显示全部楼层 · 2013-2-24 23:51:03

lim(x→∞) [ax2/(x+1)+bx]= lim(x→∞) [ax2+bx(x+1)]/(x+1)= lim(x→∞) (ax2+bx2+bx)/(x+1)= lim(x→∞) [(a+b)x2+bx]/(x+1) = 2这个极限等于2(常数)说明分子和分母都是等价的分母最大次方是1，那么分子最大次方也是1即x2的系数是0，得到a+b=0再进一步求的话lim(x→∞) bx/(x+1) = 2lim(x→∞) b/(1+1/x) = 2b/(1+0) = 2b = 2，则a = -2...

千问 · 2013-2-24 23:51:03

ax^2/(x+1)+bx=[(a+b)x^2+bx]/(x+1)lim(x→0) [(a+b)x^2+bx]/(x+1)=lim(x→0)[(a+b)x^2+bx]' /(x+1)'=bb=2,a+b=a+2...