How to solve this?

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1 Answer
Mar 15, 2018

Answer is (2) i.e. 1/sqrt2

Explanation:

lim_(x->3)(sqrt(3x)-3)/((sqrt(2x-4)-sqrt2)

As when x->3, both numerator and denominator approach 0, we can use L'ospital's rule and hence the limit is equal to

lim_(x->3)((d(sqrt(3x)-3))/(dx))/((d(sqrt(2x-4)-sqrt2))/(dx))

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

= (sqrt3/(2sqrt3))/(2/(2sqrt(2*3-4)))=sqrt3/(2sqrt3)xx(2sqrt(6-4))/2

= sqrt2/2

= 1/sqrt2

Hence answer is (2).