Sorry for not solving all the questions as it is advised here to solve only 1st question in case of multiple questions.
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give...
Sketch the space curve represented by the vector-valued function and give the orientation of the curve. r(t) = 5 cos(t)i + 5 sin(t)j + tk o op Tul Tul V - 5 y - 5
Do one problem: A or B. Z A. Use table to sketch the curve represented by the vector-valued function and give the orientation of the curve. Y *33+ t -2 -1 0 1 2 r(t)-31'i-tj+2 tk . x1-24 -3 103 124 42 10- 12 r(t)-3e'i-2Vt j +31 k 2 18 12 10 12 18 y=-t 'Z=24² or B. Represent the curve by a vector-valued function using the indicated parameter. z? = x++y?. x + 3y = 3, y = 3/4...
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1] 6 2 2 6 6 22 7. 4 2 Find its length over the given interval. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = 2x + 2xy + y Constraint: 2x + y = 200 file 40.80
14.- Sketch the curve represented by the intersection of the surfaces. Find a vector-valued function for the space curve 14.- Sketch the curve represented by the intersection of the surfaces. Find a vector-valued function for the space curve
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
Please explain all steps. Need to understand. Thanks Let C be the closed curve defined by r(t) = cos ti + 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 + x2)j + xk
PLEASE SHOW ALL WORK AND EXPLAIN BOTH PARTS. Thanks Let C be the closed curve defined by r(t) = cos ti + 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 + x2)j + xk
good evening. i need help with this calculus question. i will thumbs up your answer. Let C be the closed curve defined by r(t) = cos ti+ sin tj + sin 2tk for 0 <t<27. (a) [5 pts) Show that this curve C lies on the surface s defined by 2 = 2xry. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral s F. dr where F(x, y, z) = (y2 + cos z)i + (sin y +22)j...
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...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.