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极限存在,满足洛必达即分子=0,可得c=2,第一次洛必达
lim=lim(2a(x-1)+b-2x/2√(x²+3))/2(x-1)
=lim(2a(x-1)√(x²+3)+b√(x²+3)-x)/2(x-1)√(x²+3)
依然满足洛必达故2b-1=0,b=1/2,继续洛必达
=lim(2a√(x²+3)+2a(x-1)x/√(x²+3)+x/2√(x²+3)-1)/(2√(x²+3)+2(x-1)x/√(x²+3)
分子=4a+0+1/4-1,分母=4+0≠0,故4a+0+1/4-1=0,a=3/16
lim=lim(2a(x-1)+b-2x/2√(x²+3))/2(x-1)
=lim(2a(x-1)√(x²+3)+b√(x²+3)-x)/2(x-1)√(x²+3)
依然满足洛必达故2b-1=0,b=1/2,继续洛必达
=lim(2a√(x²+3)+2a(x-1)x/√(x²+3)+x/2√(x²+3)-1)/(2√(x²+3)+2(x-1)x/√(x²+3)
分子=4a+0+1/4-1,分母=4+0≠0,故4a+0+1/4-1=0,a=3/16
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