Choose the graph that matches the vector equation. r(t) = – ti + tj + tk,...
Choose the graph that matches the vector equation. r(t = - i + j + tk, st<4 Choose the correct answer below. QA. 08. 0C. OD. (-4... 4) 4. 4.4) I4. 4. -4)
(1) 8ketch the graph of r(t) and show the direction of increasing t 2:r, c) r(t) -3costí + 3 sin tj + tk; d) a) r(t).-ti+3, b) r(t)-< 2cos t, 5 sin t >, О r(t)- ti+ t2j + 2k t Describe the graph of r(t) 3 cos ti+5sin tj+4 cos tk (1) 8ketch the graph of r(t) and show the direction of increasing t 2:r, c) r(t) -3costí + 3 sin tj + tk; d) a) r(t).-ti+3, b) r(t)-,...
QUESTION 1 Find r' (3) if r(t) = t3i+tj + tk A. 3i + 2+ 1k B. 18 i +6j+1 k C. 9 ii+ 3j+0k D. 27 i +6j+1 k QUESTION 2 Find r' (11/2) if r(t) = 2sin(t) i + 3cos(t)j OA. -2 i + Oj 01 – 3j c.2 i + 3j D. 01 + 1 j QUESTION 3 Evaluate S 3421- 4 të jdt A. 31 - 4j i cu B.31 +4j cli - 1j Da bit...
Find the tangential and normal components of acceleration of a particle with position vector r(t) = 4 sin ti + 4 cos tj + 3tk.
Find destr(e) • u(e)] and cr(e) * u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j + tk (a) (PCE) • u(e)] (1) Find the product first, then differentiate. (ii) Apply the properties of the derivative. (b) decerce) x uct)] (1) Find the product first, then differentiate. (ii) Apply the properties of the derivative.
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
The equation for a causal full-wave rectified signal is given by c(t) = 12 sin(1 t)u(t) a) The even component of r(t) is shown by xe(t). 1) Find the equation for e(t). ve(t) = 2) From the figures 1 to 4 shown below, select the graph that matches xet). Figure: ? 3) Is ze() causal? ? 4) Is zelt) periodic? ? b) The odd component of 3(t) is shown by xo(t). 1) Find the equation for 2 (t). 2.(t) =...
Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path Cy: r(t) = ti + tj + tk, Osts 1 b. The curved path Cz: r(t) = Osts1 c. The path C, UC, consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0,0,0) (1.1.1)
Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A (0,0. 2 y- r(t)= (, ? r(t) (sin (t),t) r (t) (t, cos (2t), sin (2t)) ? v r (t) (1 +t,3t,-t) r (t) (t)i-cos (t)j+sin (t) k =COS r(t)=i+tj+k r(t) i+tj+2k r(t)= (1,cos (t).2sin (t) Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk