Concept explainers
Using Stokes's Theorem In Exercises 7-16, use Stokes’s Theorem to evaluate
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Sketch the plane curve represented by the vector-valued function and give the orientation of the curve. (8) = cos(6) +2 sin(6) O -2 y y ⓇE y yarrow_forwardLet F= LF C Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1), oriented counterclockwise as viewed from above.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(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_forward
- Calculate the directional derivative of g(x, y, z) = x In (y + z) in the direction v = 5i – 4j + 4k at the point P = (8, e, e). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dyg(8, e, e) =arrow_forwardUse Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above. (x + y?)i + (y + z?)j + (z + x2)k, C is the triangle with vertices (3, 0, 0), (0, 3, 0), and (0, 0, 3). F(x, у, z)arrow_forwardUse Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi +3zj + xk C: triangle with vertices (8, 0, 0), (0, 8, 0), (0, 0, 8)arrow_forward
- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3V2, 3V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. E) - =arrow_forwardFind r(t) u(t). r(t). u(t) r(t) = (4 cos(t), 9 sin(t), t – 4), u(t) = (18 sin(t), −8 cos(t), t²) Is the result a vector-valued function? Explain. Yes, the dot product is a vector-valued function. No, the dot product is a scalar-valued function.arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3/2) %3D (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = %3D s(t) = %3D a(t) = %3D (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D al %3D IIarrow_forward
- The 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_forwardc) 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_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 tj (V5, 2V5) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = -4 sin(t)i + 4 cos (2)j s(t) 4. -cos(1)i – 4 sin(r) a(t) = COS (b) Evaluate the velocity vector and acceleration vector of the object at the given point. -2V2 i+ 2V2jarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning