Which is the Taylor series for the function f(x) near x = 5 ?
The correct answer is (C). (A) is the generic formula and doesn't mention 5 at all. (B) put 5 in for x, but the phrase "near x = 5" means we want to substitute 5 for a, not for x. (D) has the exponents wrong - according to the formula we want to have the expression (x – 5)2, not (x2 – 5).