How do you evaluate the limit #(sqrt(x+1)-2)/(x^2-9)# as x approaches -3?

Question

Since #sqrt(x+1)# is not defined at #x=-3#, we will take limit as #x# approaches #+3# instead of #-3#

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Answer 1 · 2016-08-22T11:05:55

#1/24#.

Reqd. Limit#=lim_(xrarr 3) (sqrt(x+1)-2)/(x^2-9)#

#=lim_(xrarr 3) (sqrt(x+1)-2)/(x^2-9)xx(sqrt(x+1)+2)/(sqrt(x+1)+2)#

#=lim_(xrarr 3) (x+1-4)/((x+3)(x-3)(sqrt(x+1)+2))#

#=lim_(xrarr 3) cancel((x-3))/((x+3)cancel((x-3))(sqrt(x+1)+2))#

#=lim_(xrarr 3) 1/(x+3)xx1/(sqrt(x+1)+2)#

#=(1/6)(1/4)#

#=1/24#.