Evaluate the limit

Question

lim x→∞ x³/ ln(x)

A. 3x

B. 3

C. 3x³

D. Does not exist.

Answer 1

lim x->infinity of (x^3)/ (lnx)

= infinity/infinity

= indeterminate

Use L'Hopital's Rule

Take derivative of numerator and denominator.

= lim x->infinity of (3x^2)/ (1/x)

= lim x->infinity of (3x^3)

= infinity

The answer is (D.) Does Not Exist.

Answer 2