Find the limit... ?

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Jan 13, 2017

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Answer 1 · 2017-01-13T01:21:33

#1/2#

#sqrt(9x^2+3x)-3x=(9x^2+3x-9x^2)/(sqrt(9x^2+3x)+3x)= (3x)/(sqrt(9x^2+3x)+3x)# but

#(3x)/(sqrt(9x^2+3x)+3x)=(3x)/(3x(sqrt(1+1/(3x))+1))=1/(sqrt(1+1/(3x))+1)#

finally

#lim_(x->oo)sqrt(9x^2+3x)-3x=lim_(x->oo)1/(sqrt(1+1/(3x))+1)=1/2#