How do you find the limit of #(sqrt(x+3) - sqrt(3)) / x# as x approaches 0?

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Answer 1 · 2016-09-24T05:29:42

#" The Reqd. Lim.="sqrt3/6#.

The Reqd. Limit#=lim_(xrarr0)(sqrt(x+3)-sqrt3)/x#

#=lim_(xrarr0) (sqrt(x+3)-sqrt3)/x xx (sqrt(x+3)+sqrt3)/(sqrt(x+3)+sqrt3)#

#=lim_(xrarr0) {(sqrt(x+3)^2-sqrt3^2)}/{x(sqrt(x+3)+sqrt3)}#

#=lim_(xrarr0) (x+3-3)/{x(sqrt(x+3)+sqrt3)}#

#=lim_(xrarr0) 1/((sqrt(x+3)+sqrt3)#

#=1/(sqrt3+sqrt3)=1/(2sqrt3)=sqrt3/6.#

#:." The Reqd. Lim.="sqrt3/6#.