Find a function r(t) that describes the line or line segment. ) The line through P(4, 9, 3) and Q(1, 6, 7) A) r(1) = (4 - 3t, 9 + 4t, 3 - 31) B) r(1) = (4 + 4t, 9 - 3t. 3 - 31) C) r(t) = (4 - 3t, 9 - 3t, 3 + 41) D) r(t) = (4 - 3t, 9 - 4t, 3 + 31) Evaluate the limit. 2) lim (7 cos ti + 6 sin t j) t-+ 3n/2 A) -6j B) 6j C) 7i - 6j D) 71 3) lim (be-ti + 3e-t j) t- In 6 A) zi B) i + zi c) li zi D) - zi Find the domain of the vector-valued function. 4) r(1) = sin 3ti + evt j A ) 127 B) t > 3 C) All real numbers D) 120 Differentiate the function. 5) r(1) = (-712 - 6)i +213); A) r'(1) = (-14t)i + 112); B) r'(1) = (-14)1 + 2+ C) r'(1) = (-14t)1 - 12); 6) r(t) = (cot t)i + (csc t)j A) r'(1) = (csc2 t)i + (cot tcsc t)j B) r'(t) = (-sec2 t)i - (tan t sec t)j c) r(1) = (-csc2 t)i - (cot t csc t)j D) r'(t) = (sec2 t)i + (tan t sec t)jFind the unit tangent vector of the given curve. 7) r(t) = 315i - 1215j + 415k A) T = = 3 12 169 169 * 169 B) T = - 3 ;_ 12; 13 13 - 7k C) T = 12; 13 1 + 13+ 13 D) T= = 3 ; 12; 13 13' k * 13 8) r(t) = 2 costa + 2 sin ti- 12tk A) T = - 2 sin Sthi + 2 cos Sti . 13 13 B T - - cos 3ti + 5 sin Silj - 12k C) T = -5 73 Sin Sti + 5 + 73 COS 51) - 12 13 D) T =| 5 169 cos Sthi + 5 169 sin Sti - 12-k 169 Evaluate the integral. A) 41 + 81j + --k B) 21 - 81j + k 10 C) 41 - 81j+ 10 D) 41 - 81j + 7 . 2k 10) [(4sec2 t)i - (3 + sin t)j - (4sec t tan t)k)]at A) 41+ 2 1/2 - 371 - 4+ 4(1 - 2)k B) 41 + 2 /2 - 37t - 4+ 4(1 - 2)k 2 C) 41+ 21/2 - 3nt - 4 + 4(1 + 2)k D) 41+ 21/2 + 37 + 41; + 4(1 + 2)k If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. 11) Find the velocity vector. r(t) = (-712 - 8)i +13); A) v = (-14)i + thi B) v = (-141)i- -12 ; C) v =12\\+ (-140); D) v = (-141)i +412; 12) Find the acceleration vector. r(t) = (cos 3t)i + (5 sin t)j A) a = (-9 cos 31)i + (-5 sin t)j B) a = (9 cos 3t)i + (-5 sin t)j C) a = (-9 cos 3t)i + (-25 sin t)j D) a = (-3 cos 3t)i + (5 sin t)j The position vector of a particle is r(t). Find the requested vector. 13) The velocity at t = 0 for r(t) = cos(2t)i + 7In(t - 3)j - --k A) v(0) = -21 - -i B) v(0) = 21 - 2j C) vo) =-zi D) v(0) = zi