Gradients and radial fields Prove that for a real number p. with
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- Let f = f(x, y, z) be a sufficiently smooth scalar function and F = Vƒ be the gradient acting on f. Which of the following expressions are meaningful? Of those that are, which are necessarily zero? Show your detailed justifications. (a) V· (Vf) (b) V(V × f) (c) V × (V · F) (d) V. (V × F)arrow_forwardDetermine if the vector (cos y, y -xsin y) is a gradient. If it is a gradient, determine the function from which this gradient vector was obtained.arrow_forwardSuppose f(x,y)=x/y, P=(0,−1) and v=3i+3j. A. Find the gradient of f.∇f= ____i+____jNote: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P.(∇f)(P)= ____i+____j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v.Duf=?Note: Your answer should be a number D. Find the maximum rate of change of f at P.maximum rate of change of f at P=? Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P.u= ____i+____jNote: Your answers should be numbersarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,