How do you find the limit of #(2x) / (x+7sqrt(x))# as x approaches 0?

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Answer 1 · 2016-10-09T22:56:42

#lim_(xrarr0)(2x)/(x+7sqrtx)=0#

#lim_(xrarr0)(2x)/(x+7sqrtx)#

Factor #sqrtx# from the denominator:

#=lim_(xrarr0)(2x)/(sqrtx(sqrtx+7))#

Dividing #sqrtx/sqrtx#:

#=lim_(xrarr0)(2sqrtx)/(sqrtx+7)#

Now we can evaluate the limit without having a denominator of #0#:

#=(2sqrt0)/(sqrt0+7)=0/7=0#