(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...
Choose the graph that matches the vector equation. r(t) = – ti + tj + tk, Osts 1 Choose the correct answer below. A. B. C. D. Az AZ (-1, 1, 1) (1, 1, 1) 1 A у X X X |(1, 1, -1) X
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
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...
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. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
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...
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
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...
Question No. 1 Sketch the graph of r(t) and show the direction of increasing t. = costi + sint; + 6k