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if-lim-x-1-x-2-ax-b-x-1-5-faind-volve-of-a-b-




Question Number 169204 by mathlove last updated on 26/Apr/22
if lim_(x→1) ((x^2 −ax+b)/(x−1))=5  faind volve of a+b=?
iflimx1x2ax+bx1=5faindvolveofa+b=?
Commented by Rasheed.Sindhi last updated on 26/Apr/22
Do you mean       lim_(x→1) ((x^2 −ax+b)/(x−1))=5   ?
Doyoumeanlimx1x2ax+bx1=5?
Commented by infinityaction last updated on 26/Apr/22
      1^(2 ) −a×1 + b  = 0        b    =  1−a     use l hospital rule          lim_(x→1)  ((2x−a)/1) = 5            2×1 − a =5               a =  −3      ∴     b  = a−1          b = −3 −1 = −4     then        a+b  =  −4 −3       a+b  =  −7
12a×1+b=0b=1auselhospitalrulelimx12xa1=52×1a=5a=3b=a1b=31=4thena+b=43a+b=7
Answered by Rasheed.Sindhi last updated on 26/Apr/22
If you mean:  lim_(x→1) ((x^2 −ax+b)/(x−1))=5  Let x^2 −ax+b=(x−1)(x−p)  lim_(x→1) (((x−1)(x−p))/(x−1))=5  lim_(x→1)  (x−p)=5         1−p=5           p=−4  (x−1)(x−p)=(x−1)(x+4)=x^2 −ax+b  x^2 +3x−4=x^2 −ax+b   Comparing coefficients:        a=−3,b=−4  a+b=−7
Ifyoumean:limx1x2ax+bx1=5Letx2ax+b=(x1)(xp)limx1(x1)(xp)x1=5limx1(xp)=51p=5p=4(x1)(xp)=(x1)(x+4)=x2ax+bx2+3x4=x2ax+bComparingcoefficients:a=3,b=4a+b=7
Commented by mathlove last updated on 26/Apr/22
yes x→1
yesx1
Commented by mathlove last updated on 26/Apr/22
thanks sir alot of
thankssiralotof

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