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(22 - y2 + 2)ds, here C is the curve r(t) = (3 cost, 3 sint, 4t) with 0 <t<2.
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2 + y2 + 22. Evaluate (12 pts) f(,y,z)ds.
4. Evaluate Sl y(+12) ds, where S = {(1,y,z) : 2 = 4 – r?,05152,0 <ys 5).
:) IS (x+y+z)ds X-1 (b): Find the work done by F over the curve in the direction of increasing t, where F =< x² + y, y2 + 1, ze >, r(t) =< cost, sint,t/27 >, Osts 27. y-2=2-3 =+ C) -1-2 I-3
QUESTION 16 Find the arc length of the helix traced by r(t) = <p cost, p sint,pt> for Osts2.when the value of p-3. QUESTION 17 The equation passes through the points P (6,1,-1). Q(0, -2.0) and R(1.-1.7) is given by ax+by+czek Follow the steps below and find value of k. Lick Save and Submit to save and submit. Click Save All Answers to save all answers. A ) 17 F5 F4 F3 F2 % 7
Let C be the helix parametrized by r(t) = (cost, sint,t), 0 <t<7/2 in R3. Compute the flow of the vector field (x – yz sin xyz, zey? – zx sin xyz, yeyz – xy sin xyz) along C.
2. Compute | F. ds for each of the vector fields F and paths r given below: (b) Ple:) - (a ) and re) – () witte (0.1 Fler,1,2) = ( and r(t) = ( ) with t e (0, 2). F(x, y, z) = | 22 and r(t) = with t€ (0,2). F(x, y, z) = sin Cos y 32 and r(t) = -t with t € (0,1). (a) F(x, y, z) = | Vies:)-( .) --( * )-464...
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Evaluate e, ds where C is given by α(t)-(et cost, et sint, t), 0-t-2T. π.
Evaluate e, ds where C is given by α(t)-(et cost, et sint, t), 0-t-2T. π.
EXERCISE 1.64. For the helix in Example 1.3, defined as y(t) (cost, sint,t), t E R, com defined as (t) (cos t, sin t,-t), te R. Describe the visual difference between a helix with positive torsion and a helix with negative torsion. pute the torsion function. Do the same for the helix
EXERCISE 1.64. For the helix in Example 1.3, defined as y(t) (cost, sint,t), t E R, com defined as (t) (cos t, sin t,-t), te R. Describe the...
3. Let C be the curve r(t) = < sint, cost, t>,0 sts 1/2. Evaluate the line integral S ry ryds. 1/V2. 1/2, V2, 0,