If ,
lim ₓ→ₐ ( αx² - β )/( x - 3 ) = 12 then find the value of α and β
Answers
Answer:
Step-by-step explanation:
We require that:
L=lim x→a (ax²−b/x−3)=12
As the denominator is zero when
x=3
then the limit can only exist if the numerator has a factor
(x−3)
, Then by the remainder theorem, the numerator has a root
x=3
, let us denote the other root by
α
then we have:
L=limx→a
(x−α)(x−3)/x−3
=limx →a
(x−3)=0
x=3
Given this we can now write the numerator as:
ax²−b≡(x+3)(x−3)=x²−9
And by comparing coefficients we have get answer
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L=lim x→a (ax²−b/x−3)=12
As the denominator is zero when
x=3
then the limit can only exist if the numerator has a factor
(x−3)
, Then by the remainder theorem, the numerator has a root
x=3
, let us denote the other root by
α
then we have:
L=limx→a
(x−α)(x−3)/x−3
=limx →a
(x−3)=0
x=3
Given this we can now write the numerator as:
ax²−b≡(x+3)(x−3)=x²−9
And by comparing coefficients we have get answer