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Finding an Antiderivative In Exercises 53-58, find r(t) that satisfies the initial condition(s).
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Chapter 12 Solutions
Multivariable Calculus - With WebAssign
- Proof of Product Rule By expressing u in terms of its compo- nents, prove that d (f(1)u(t)) = f'(1)u(t) + f(t)u'(1). dtarrow_forwardVr² + y² + z² at Find the linear approximation of the function f(x, Y, z) (3, 2,6) and use it to approximate the number V(3.02)² + (1.97)² + (5.99)².arrow_forwardCalculus Answer, please don't use italics, as I do not understand it Calculate the work that a constant force field F does on a particle that moves uniformly once along the path of the curve x2 + y2 = 1.How much is the work now worth if we take F(x, y) = (αx, αy), where α is any positive constant?arrow_forward
- Prove Theorem (A + B )T = AT + B Tarrow_forwardDetermine wether the function f(x, y) = x3 + 4xy2 + y3 is homogeneous, and if it is, determine its degree. A function f(x, y) is homogeneous of degree n if f(tx, ty) = tnf(x, y)arrow_forwardCalculus Answer Calculate the work that a constant force field F does on a particle that moves uniformly once along the path of the curve x2 + y2 = 1.How much is the work now worth if we take F(x, y) = (αx, αy), where α is any positive constant?arrow_forward
- af find given f (x, y) = e + 2xy² - 4y at (0,3) > ду O-12 O-7 O 8 O4arrow_forwardCurl of a vedor point field = i+it k is point field ? = xi+ j+ zk is %3D 2x it 24j+2zk 2x+24+ 2arrow_forwardDetermine wether the function f(x, y) = tan(x + y) is homogeneous, and if it is, determine its degree. A function f(x, y) is homogeneous of degree n if f(tx, ty) = tnf(x, y)arrow_forward
- Determine wether the function f(x, y) = ex/y is homogeneous, and if it is, determine its degree. A function f(x, y) is homogeneous of degree n if f(tx, ty) = tnf(x, y)arrow_forwardFind div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k. 2x - 1 O 2xy - 1 O 2xi-k O 2xy i+ karrow_forwardLogarithmic potential Consider the potential function 9(x, y, z) = In 1 (x² + y? + z?) = In |r|, where r = (x, y, z). a. Show that the gradient field associated with o is (x, y, z) r F = r|2 x + y? + ? b. Show that ffs F -n dS = 4ma, where S is the surface of a sphere of radius a centered at the origin. c. Compute div F. d. Note that F is undefined at the origin, so the Divergence Theorem does not apply directly. Evaluate the volume integralarrow_forward
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- 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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