Sketch the space curve represented by the vector-valued function and give the orientation of the curve....
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give the orientation of the curve. 2 9. r(t) = (n cost, i sin ) 10. r(t) = (1 + 2.12 - 1) 11. r(t) = (1 + 1)i + (31 - 1)j + 2tk 12. r(t) = 2 cos ti + tj + 2 sin tk 29 12. r(t) = 2 cos ti + tj + 2 sin tk
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
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...
Evaluate the integral Vs««, », z) ds over the surface o represented by the vector-valued function " (u, v). sus2,05vs f(x, y, z) = 3xyz; r(u, v) = u cos vi+ u sin vj +4u k (1 sus 2 Enter the exact answer. 15x,y,z) as = ? Edit
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
3.) Sketch the curve represented by the parametric equation and indicate the orientation of the curve. Also, write the corresponding rectangular equations by eliminating the parameter. x = sec , y = cos 0, 0<O< 1/2, 7/2 <OS
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued function r (u, v). -; r(u, v) = 7 u cos vi+7 u sin vj + 7 u’ k (0 sus sin v, 0 SV ST) 9 f (x, y, z) = 49 + 4x2 + 4y2 Enter the exact answer. 144 f (x, y, z) dS = ? Edit 0 action Attornten of 1
Solve C and D part please
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.(Can you name the curve?) (a) r = sin 0, y = cos, - SOST (b) x = 4 sect and y = 3 tant 3 3 (c) r=-1+ z sint and y = cost for -A <t <3 (d) x = cosht and y cosh 3t (no need to sketch...
Sketch the curve represented by the parametric equations (indicate the orientation of the curve) and B) eliminate the parameter and write the resulting rectangular equation whose graph represents the curve. Adjust the domain of the rectangular equation, if necessary. x = t + 4 and y = t2
Evaluate the line integral ∫C.F·dr, where C is given by the vector function r(t).F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t3 i- t3j + tk, 0 ≤ t ≤ 1 .