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Using Stokes’s Theorem In Exercises 9–18, use Stokes’sTheorem to evaluate
C:triangle with vertices
Using Stokes’s Theorem In Exercises 9–18, use Stokes’s Theorem to evaluate
C: triangle with vertices
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Chapter 15 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
- Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(0, 0, 0), Q(4, 2, 4) r(t) = %3D Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)arrow_forward3.use Greens theorem f (1 + x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0) ,(1,3) oriented clockwise Hinit (3) da A (Uの)arrow_forwardRepresent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(0, 0, 0), Q(2, 7, 5) r(t) = Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list.)arrow_forward
- c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x=2, x=-2, y=0 and y=4arrow_forwardbo Find (xT x)" xT y where, b2 40 57 112 45 54 118 50 54 128 55 60 121 60 66 126 65 59 136 70 61 144 75 58 142 80 59 149 85 56 165 S SINARLINEarrow_forwarda) A three dimensional motion of an object is given by the vector function r(t) = 4 cos t i+ 4 sin tj+5 k. Sketch the motion of the object when 0arrow_forwardSketch the plane curve represented by the vector-valued function and give the orientation of the curve. r(0) = cos(0)i + 6 sin(0)j O O -2 -2 y 5 -5 y -5 2 2 6 X X -6 -4 -2 -6 -4 -2 y 2 2 4 4 6 X Xarrow_forwardFind a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 4 cos ti + 4 sin t (2V2,2V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the objeot. v(t) s(t) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point.arrow_forwardarrow_back_iosarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage