Evaluate the value of ((x+4)^2-4)/x as x approaches to 0?

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Answer 1 · 2018-05-05T11:03:12

Does not exist.

#lim_(xrarr0)((x+4)^2-4)/x# #=^((12/0))?#

#lim_(xrarr0^+)((x+4)^2-4)/x# #=^((12/0^(+)))# #+oo#

#lim_(xrarr0^(-))((x+4)^2-4)/x# #=^((12/0^(-)))# #-oo#

Graphical help enter image source here

Answer 2 · 2018-05-05T11:08:08

#4#

Let,

#lim_(x->0)f(x)=lim_(x->0)((x+4)^2-4)/x#

If #x->0^-,then,1/x->-oo=>lim_(x->0^-) f(x)to -oo and#

If #x->0^+,then,1/x->+oo=>lim_(x->0^+) f(x)to +oo#

Hence,

#lim_(x to 0) f(x)# does not exist.