Question

How do you find the limit of `(x+1)/(x^4-1)` as x approaches `-1^-`?

Answer 1

The denominator canbe factored as follows

`x^4-1=(x^2-1)*(x^2+1)=(x-1)(x+1)(x^2+1)`

Hence

#lim_(x->-1) (x+1)/(x^4-1)=lim_(x->-1) (x+1)/[(x-1)*(x+1)*(x^2+1)]= lim_(x->-1) 1/[(x-1)*(1+x^2)]=-1/4#