Concept explainers
(a) Use Stokes’ Theorem to evaluate
(b) Graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve
(c) Find parametric equations for
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Chapter 16 Solutions
Calculus 8th Edition
- 1 x² + 4y2) 10 8) Given z =f (x,y) =1- „Find : a)The vector function, normal to the surface of f at (x,y).arrow_forwardFind a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0 and the plane 2x -z = 0.arrow_forwardFind a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.arrow_forward
- The paraboloid z = 8 − x − x2 − 4y2 intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3, 2, −20). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)arrow_forwardThe paraboloid z = 6 - x - x² – 2y² intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3, 3, -24). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)arrow_forwardFind the parametric equations for the line through the point of intersection of the lines L1:x = 2 + 3t, y = 5t, z = 2 +t and L2: x = 3+ 2t, y = 4+ t, z = 5 – 2t and perpendicular to the plane 3x – 4y + 2z = 7arrow_forward
- . What is the scalar equation of the xy plane?arrow_forwardFind the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4 intersect. r(t) + tarrow_forwardc) Use Stokes' theorem to evaluate ſF dr where F = 22i+ yJ + xk and C is the triangle with vertices (2,0, 0), (0, 2,0) and (0,0, 2) with anticlockwise direction when viewed from above.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,