How do you find the limit of #f(x) = (x^2 - 1) / ( x + 1) ^2# as x approaches -1?

1 Answer
Mia
Oct 9, 2016

#lim_(x->-1)f(x)=-oo#

Explanation:

Since when substituting #-1# in the given function there is indeterminate value #0/0#
We have to think about some algebraic

#lim_(x->-1)f(x)=lim_(x->-1)(x^2-1)/(x+1)^2#
#lim_(x->-1)f(x)=lim_(x->-1)((x-1)(x+1))/(x+1)^2#

We simplify #x+1#
#lim_(x->-1)f(x)=lim_(x->-1)(x-1)/(x+1)#
#lim_(x->-1)f(x)=lim_(x->-1)(-1-1)/(-1+1)#
#lim_(x->-1)f(x)=lim_(x->-1)-2/0#
#lim_(x->-1)f(x)=-oo#

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