lim x->3   ( x-3/(x^2-4x+3) ) lim x->3   ( x-3)/(x^2-4x+3)

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We can find the limit by applying L'Hopital's rule:

if f(c) = g(c) = 0, then lim f(x)/g(x), x->c = lim f'(x)/g'(x), x->c

f(x) = x - 3 --> f'(x) = 1 --> f'(3) = 1

g(x) = x^2 - 4x + 3  --> g'(x) = 2x - 4 --> g'(3) = 2

lim f(x)/g(x), x->3 = lim f'(3)/g'(3) = 1/2

 

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