lim (x^2+ax+b)/(x-2)=3,求a,b的值?x趋于2

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lim (x^2+ax+b)/(x-2)=3,求a,b的值?x趋于2
lim (x^2+ax+b)/(x-2)=3,求a,b的值?
x趋于2

lim (x^2+ax+b)/(x-2)=3,求a,b的值?x趋于2
∵lim (x^2+ax+b)/(x-2)=3
∵x=2时,有x+1=3
∴x^2+ax+b=(x-2)(x+1)=x^2-x-2
∴a=-1,b=-2

上面的(x^2+ax+b)分解因式后肯定有一个因式是x-2，否则分母趋近于0，分子不趋近于0，没有极限；
所以上面的(x^2+ax+b)可以分解成（x+x1）*(x-2)/(x-2)->x+x1当x趋近于2，极限是3，x1=3-2=1;
所以(x^2+ax+b)就是（x+1）*(x-2)也就是x²-x-2;对比（x^2+ax+b)则a=-1;b=-2;
a=-1;...

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令x² + ax + b = (x - 2)(x - M)
x² + ax + b = x² - (2 + M)x + 2M
- 2 - M = a ===> M = - 2 - a
2M = b ===> M = b/2

lim(x→2) (x² + ax + b)/(x - 2) = 3

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令x² + ax + b = (x - 2)(x - M)
x² + ax + b = x² - (2 + M)x + 2M
- 2 - M = a ===> M = - 2 - a
2M = b ===> M = b/2

lim(x→2) (x² + ax + b)/(x - 2) = 3
lim(x→2) (x - 2)(x - M)/(x - 2) = 3
lim(x→2) x - M = 3
==> lim(x→2) x - (- 2 - a) = 3
==> 2 + 2 + a = 3 ==> a = - 1
==> lim(x→2) x - b/2 = 3
==> 2 - b/2 = 3 ==> b = - 2
∴a = - 1，b = - 2

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lim (x^2+ax+b)/(x-2)=lim (x^2-4X+4+4X-4+ax+b)/(x-2)=lim[ (x-2)^2+(a+4)x+(b-4)]/(x-2)
=lim(x-2)+lim[(a+4)x+(b-4)]/(x-2)=lim(x-2)+lim[(a+4)(x-2)+(b-4)+2(a+4)]/(x-2)
=lim(x-2)+lim(a+4)+lim[(b-4)+2(a+4)]/(x-2)=lim(x-2)+lim(a+4)+lim(2a+b+4)/(x-2)=3
所以a+4=3，2a+b+4=0
所以a=-1，b=-2

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