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

2 Answers
May 5, 2018

Does not exist.

Explanation:

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

  • If #x->0^+# , #x>0# then

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

  • If #x->0^-#, #x<0# then

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

Graphical help enter image source here

May 5, 2018

#4#

Explanation:

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.