- The Taylor polynomial of order 3 at x = 0 for (1 + x)p, where p is a constant, is
(A) 1 + px + p(p − 1)x^2 + p(p − 1)(p − 2)x^3
(B)
(C)
(D)
(E) none of these
- The Taylor series for ln (1 + 2x) about x = 0 is
(A)
(B) 2 x − 2x^2 + 8x^3 − 16x^4 + · · ·
(C) 2 x − 4x^2 + 16x^3 + · · ·
(D)
(E)
- The set of all values of x for which converges is
(A) only x = 0
(B) |x| = 2
(C) −2 < x < 2
(D) |x| > 2
(E) none of these
- The third-order Taylor polynomial P 3 (x) for sin x about is
(A)
(B)
(C)
(D)
(E)
- Let h be a function for which all derivatives exist at x = 1. If h(1) = h′ (1) = h′′ (1) = h′′′ (1) = 6,
which third-degree polynomial best approximates h there?
(A) 6 + 6x + 6x^2 + 6x^3
(B) 6 + 6(x − 1) + 6(x − 1)^2 + 6(x − 1)^3
