Multiple choice general knowledge math & puzzles what is the limit as x approaches 0 of tan x – x / x cubed 3 0 1/3 DNE Reveal answer Fill a bubble to check yourself C Correct answer Explanation Using the Taylor series expansion, tan(x) = x + x^3/3 + ... near x = 0. Substituting: tan(x) - x = x^3/3. Dividing by x^3 gives 1/3. The limit exists and equals 1/3 as x approaches 0.