Evaluate the limit: lim (x->0) (sin(x) - x + x^3/6) / x^5
Correct: A
Using the Taylor series expansion for sin(x) around x=0: sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ... So, sin(x) - x + x^3/6 = sin(x) - x + x^3/3! = x^5/5! - x^7/7! + ... Then, (sin(x) - x + x^3/6) / x^5 = 1/5! - x^2/7! + ... As x approaches 0, the limit is 1/5! = 1/120.