Concept explainers
Tangent Curves In Exercises 39-42, use agraphing utility to graph the family of curvestangent to the force field.
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
Multivariable Calculus
- Consider the force field and circle defined below. F(x,y)=x2 i+xyj x2 +y2 =36 (a) Find the work done by the force field on a particle that moves once around the circle oriented in the clockwise direction. (b) Use a computer algebra system to graph the force field and circle on the same screen.arrow_forwardFlux of a vector field? Let S be a closed surface consisting of a paraboloid (z = x²+y²), with (0≤z≤1), and capped by the disc (x²+y² ≤1) on the plane (z=1). Determine the flow of the vector field F (x,y,z) = zj − yk, in the direction that points out across the surface S.arrow_forwardLine integrals of vector fields in the plane Given the followingvector fields and oriented curves C, evaluate ∫C F ⋅ T ds. F = ⟨x, y⟩ on the parabola r(t) = ⟨4t, t2⟩ , for 0 ≤ t ≤ 1arrow_forward
- Work integrals Given the force field F, find the work required to move an object on the given oriented curve. F = ⟨y, -x⟩ on the line segment from (1, 2) to (0, 0) followedby the line segment from (0, 0) to (0, 4)arrow_forwardWork integrals Given the force field F, find the work required to move an object on the given oriented curve. F = ⟨y, x⟩ on the parabola y = 2x2 from (0, 0) to (2, 8)arrow_forwardSalt water with a density of d = 0.25 g/cm2 flows over the curve r(t) = sqrt(t)i + tj, 0<= t<= 4, according to the vector field F = dv, where v = xyi + (y - x)j is a velocity field measured in centimeters per second. Find the flow of F over the curve r(t).arrow_forward
- Work integrals Given the force field F, find the work required to move an object on the given oriented curve. F = ⟨y, -x⟩ on the line segment y = 10 - 2x from (1, 8) to (3, 4)arrow_forwardLine integrals of vector fields in the plane Given the followingvector fields and oriented curves C, evaluate ∫C F ⋅ T ds. F = ⟨-y, x⟩ on the parabola y = x2 from (0, 0) to (1, 1)arrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C.F = xy i + x j; C is the triangle with vertices at (0, 0), (4, 0), and (0, 2)arrow_forward
- use Green’s Theorem to find the counterclock-wise circulation and outward flux for the field F and curve C. F = (x + y)i - (x2 + y2 )j C: The triangle bounded by y = 0, x = 1, and y = xarrow_forwardLine integrals of vector fields in the plane Given the followingvector fields and oriented curves C, evaluate ∫C F ⋅ T ds.arrow_forwardLine integrals of vector fields in the plane Given the followingvector fields and oriented curves C, evaluate ∫C F ⋅ T ds. F = ⟨y, x⟩ on the line segment from (1, 1) to (5, 10)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage