lim x->2 1/(x^2-4)^1/3

Question

limit of a function if it exists , lim x->2  1 (x^2-4)^1/3

Answer 1

Let x=2+δ, then x²=4+4δ approx if δ is very small. x²-4=4δ approx.

(x²-4)^-⅓=1/(4δ)^⅓. As δ→0, x→2 and lim as x→2 of (x²-4)^-⅓→∞, so the limit is undefined.