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# lim (x->2) (ax^2 - b)/(x-2) = 4 ; Find a and b .?

lim (x->2) (ax^2 - b)/(x-2) = 4 ; Find the solution of a and b .

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- s kLv 79 years agoFavorite Answer
As x -> 2, x - 2 -> 0. So for the limit to exist, ax^2 - b -> 0 as well.

By l'Hopital, then,

lim_{x->2} (ax^2 - b)/(x - 2)

= lim_{x->2} 2ax = 4.

So a = 1.

lim_{x->2} x^2 - b = 0.

So b = 4.

- Elizabeth MLv 79 years ago
sub x=u+2 and lim = lim u->0 [[a(u+2)^2-b]/u]

=lim u->0[au+4a +(4a-b)/u] and to equal 4 requires 4a=4 and 4a-b=0

and you can now complete.

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