R = 1 R = 00 + R = 00 7! 1 1-x et = 00 = Σ. 00 Σ= 1 + x + 1-0 n-On! = sin x = COS X = 00 1 + Σ (-1)" -0 Σ x 1! + x2m+1 (2n + 1)! x2m (-1)" (2n)! 1-0 00 tan-¹x = Σ(-1)". 7-0 00 (1 + x) = Σ 11-0 = 1 - 3! x + 3! 5! - + + 6! x2+1 = x - + - 2n + 1 k k(k-1) x" = 1 + kx + + n 2! + k(k-1)(k - 2) 3! R = 00 R = 1 R = 1

Express f(0) = cos 20 + 4(sin 20)² + 1 as a sum of powers of sin 0. 1. f(0) = 2 – 16 sin? 0 + 14 sin“ 0 2. f(0) = 2– 14 sin? 0 – 16 sinª 0 3. f(0) = 2+14 sin² 0 + 16 sinª 0 4. f(0) = 2 – 14 sin? 0 + 16 sin' 0 5. f(0) * 0 = 2+14 sin? 0 – 16 sin -

Let f"(x) = x'/A cos(x), /(0) = 2, and f(1) = 2. Is it true or false that 7=-73+ cos(x) + 28 19-28cos(1) 28 True Felse

Let F(t) = 4t*i + 2 sin(5t) j+ 3e“k and G(t) = - (cos(3t)) i – j+ k , find F(t) · G(t). 10 sin(5t) А. e)i- (20+3e cos(3t)) j + (-4tª + 2 sin(5t) cos(3t)) k В. — 414 cos(3t)і — 2 sin(st) j + 15et -k t4 15e4t с. — 4t сos(3t) — 2 sin(st) + t4 15e4t -4t“ cos(3t) – 2 sin(5t) + j t4 D. 10 sin(5t) + 3et – (20 + 3e“ cos(3t)) + (-4t“) + 2 sin(5t) cos(3t) t4