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Scalar line
a. Find a parametric description for C in the form
b. Evaluate
c. Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.
17.
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Chapter 14 Solutions
Calculus: Early Transcendentals, 2nd Edition
- Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 4 and z = 5xy. (Use symbolic notation and fractions where needed. Use hyperbolic cosine for parametrization x variable.) x(t) = y(t) = z(t) =arrow_forwardFind equations for all the planes that intersect the y-axis at y =1 and the z-axis at z =2, and are tangent to the sphere (x−2)^2 + y^2 +z^2 =4. Do not use calculus.arrow_forwardUse sine and cosine to parametrize the intersection of the surfaces x² + y² = 16 and z = 4x³. r(t) =arrow_forward
- Consider the complex function f(z) = . Describe the level curves Zarrow_forwardUse hyperbolic functions to parametrize the intersection of the surfaces x2 - y = 9 and z = 5xy. (Use symbolic notation and fractions where needed. Use hyperbolic cosine for parametrization of x = 3. cosh(t)) x(t) = y(t) : z(t) =arrow_forwardFind an expression for a unit vector normal to the surface x = 10 sin (v) , y = u, z = 10 cos (v) at the image of a point (u, v) for 0arrow_forwardDisplacement d→1 is in the yz plane 62.8 o from the positive direction of the y axis, has a positive z component, and has a magnitude of 5.10 m. Displacement d→2 is in the xz plane 37.0 o from the positive direction of the x axis, has a positive z component, and has magnitude 0.900 m. What are (a) d→1⋅d→2 , (b) the x component of d→1×d→2 , (c) the y component of d→1×d→2 , (d) the z component of d→1×d→2 , and (e) the angle between d→1 and d→2 ?arrow_forwardStokes' Theorem (1.50) Given F = x²yi – yj. Find (a) V x F (b) Ss F- da over a rectangle bounded by the lines x = 0, x = b, y = 0, and y = c. (c) fc ▼ x F. dr around the rectangle of part (b).arrow_forwardClassify and sketch the surface x − y2 − 4z2 = 0.arrow_forwardfind curl (curl F) = V x (V X F).arrow_forward2.Proof that any tangent plane for the surface F( F) point = 0 passses through a fixedarrow_forwardPath of steepest descent Consider each of the following surfaces and the point P on the surface. a. Find the gradient of ƒ. b. Let C’ be the path of steepest descent on the surface beginning at P, and let C be the projection of C’ on the xy-plane. Find an equation of C in the xy-plane. c. Find parametric equations for the path C’ on the surface. ƒ(x, y) = y + x (a plane); P(2, 2, 4)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- 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
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