Evaluating a Flux Integral In Exercises 25-30, find the flux of F across S,
where N is the upward unit normal
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
- EXERCISE 5 The temperature is T degrees at any point (x, y, z) in three-dimensional space and T(x,y, z) = 1/(x² + y² + z² + 3). %3D Distance is measured in inches. (a) Find the rate of change of the temperature at the point (3, –2, 2) in the direction of the vector –2 i+3j-6k. (6) Find the direction and magnitude of the greatest rate of change of T at (3,–2,2). 14arrow_forwardProve the properties of the vector functions F and G and the scalar function f.arrow_forwardLet V={f: R→R: fis continuous}. V forms a vector space under the "usual" addition and scalar multiplication. What is the zero vector (ie, additive identity) of this vector space?arrow_forward
- What is the geometrical meaning of an integral of a vector function?arrow_forwardGravitational potential The potential function for the gravitational force field due to a mass M at the origin acting on a mass m is φ = GMm/ | r | , where r = ⟨x, y, z⟩ is the position vector of the mass m, and G is the gravitational constant.a. Compute the gravitational force field F = -∇φ .b. Show that the field is irrotational; that is, show that ∇ x F = 0.arrow_forwardCompute the flux of the vector field F(x, y, z) = 3i + 2j + 2k through the rectangular region with corners at (1, 0, 0), (1, 1, 0), (1, 1, 2), and (1, 0, 2) oriented in the positive x- direction, as shown in the figure. Flux = (Drag to rotate)arrow_forward
- 人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT Find the integral of the vector function F(t)=(f.,cost)arrow_forwardSubject differential geometry Let X(u,v)=(vcosu,vsinu,u) be the coordinate patch of a surface of M. A) find a normal and tangent vector field of M on patch X B) q=(1,0,1) is the point on this patch?why? C) find the tangent plane of the TpM at the point p=(0,0,0) of Marrow_forwardCompute the flux of the vector field F(x, y, z) = 3i +2j+ 2k through the rectangular region with corners at (1, 0, 0), (1, 1, 0), (1, 1, 2), and (1, 0, 2) oriented in the positive x- direction, as shown in the figure. Flux =arrow_forward
- Sketch the vector field. F(x, y) =〈y, 1〉arrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C. F= (x- y)i + (x+ y)j; C is the triangle with vertices at (0,0), (10,0), and (0,5) O A. 0 В. 250 ОС. 100 D. 50arrow_forwardFind the maximum rate of change of f(x, y, z) = x + y/z at the point (1, 1, –5) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs:arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning