Consider lim ln2x3 as x infinity Let u 2x3 and note that a

Consider lim ln(2/x³) as x -> infinity. Let u = (2/x³) and note that as x -> infinity, u -> 0+. We can rewrite this limit in terms of u only, as lim lnu  as u-> 0+.

What is the value of this limit?

Solution

let g(X)= 2/x3, f(u)=log(u)

lim x->infinity (2/x3) = 0 ( as by rule lim x->infinity(c/x^a)=0)

therefore lim u ->0 (log(u))= - infinity( by chain rule)

so the limit will be - infinity