How do I find the asymptotes (HA and VA) of f(x)=ln(1+x^3) using limits of infinity?

1 Answer
Apr 13, 2018

We have a vertical asymptote #x=-1# but no horizontal asymptote.

Explanation:

Observe that for we cannot have a logarithm of a negative number. Further as #(1+x^3)->0_+#, #y->-oo#.

Hence, as #y->-oo#, #1+x^3->e^(-oo)#

or #1+x^3->0# i.e. #x->-1#

Hence, we have a vertical asymptote #x=-1#.

But as #x->oo# (note we cannot have #x<-1#), #ln(1+x^3)# continues to increase,

Hence we do not have a horizontal asymptote.