Which is the Taylor series for the function *f*(*x*) near *x* = 5 ?

(A)

(B)

(C)

(D)

Answer

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 (*x*^{2} – 5).