Question #06cb7

1 Answer
mason m
Aug 31, 2017

#3#

Explanation:

Note that #x^2-4=(x+2)(x-2)#:

#lim_(xrarr2^+)(sqrt(x^2-4)+sqrt(x-2))/sqrt(x-2)=lim_(xrarr2^+)(sqrt(x+2)sqrt(x-2)+sqrt(x-2))/sqrt(x-2)#

Dividing through by #sqrt(x-2)#:

#=lim_(xrarr2^+)sqrt(x+2)+1=sqrt(2+2)+1=3#

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