Limit Value=?

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1 Answer
Cesareo R.
Mar 6, 2018

(2)

Explanation:

(sqrt(3x)-3)/(sqrt(2x-4)-sqrt2) =(sqrt(3x)-3)/(sqrt(2x-4)-sqrt2) ((sqrt(2x-4)+sqrt2)/(sqrt(2x-4)+sqrt2))=

=((sqrt(3x)-3)(sqrt(2x-4)+sqrt2))/(2x-4-2) =((sqrt(3x)-3)(sqrt(2x-4)+sqrt2))/(2x-6)

but

(sqrt(3x)-3)/(2x-6) = (sqrt3(sqrtx-sqrt3))/(2((sqrtx)^2-(sqrt3)^2)) = sqrt3/2 1/(sqrtx+sqrt3)

so

lim_(x->3)(sqrt(3x)-3)/(sqrt(2x-4)-sqrt2) =lim_(x->3)(sqrt3/2)(sqrt(2x-4)+sqrt2)/(sqrtx+sqrt3) = 1/sqrt2

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