确定常数a,b,c使lim(x→1)[(a(x-1)^2+b(x-1)+c-√(x^2+3))/(x-1)^2=0成立.

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/20 02:20:25

lim(x→1)[(a(x-1)^2+b(x-1)+c-√(x^2+3))/(x-1)^2=0
lim(x→1)[(a(x-1)^2+b(x-1)+c-√(x^2+3))=0
c-2=0,c=2
lim(x→1)[(a(x-1)^2+b(x-1)+2-√(x^2+3))/(x-1)^2=0
罗比达法则
lim(x→1)[(2a(x-1)+b-x/√(x^2+3))/2(x-1)=0
lim(x→1)[(2a(x-1)+b-x/√(x^2+3))=0
b-1/2=0,b=0.5
罗比达法则
lim(x→1)[(2a-[[√(x^2+3)-x^2/√(x^2+3)]/(x^2+3)])/2=0
lim(x→1)[(2a-[[√(x^2+3)-x^2/√(x^2+3)]/(x^2+3)])=0
2a-3/8=0
a=3/16

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