Gradient fields Find the gradient field F = ▿ϕ for the potential function ϕ. Sketch a few level curves of ϕ and a few
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- - 40 Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9ej- e "k. Compute the derivative of the following function. u(t) - v(t) z5 (1 Select the correct choice below and fill in the answer box(es) to complete your choice. z6( O A. The derivative is the scalar function actice Di+k. O B. The derivative is the vector-valued function i+ st 2 ( uiz 7 (1 uiz 8 (1 Help me solve this View an example Get more help - uiz 9 (1 Practice Test3arrow_forwardFind the gradient of the function at the given point. Function Point f(x, y, z) = V x? + y2 + z? (7, 8, 5) Vf(7, 8, 5) = Find the maximum value of the directional derivative at the given point.arrow_forwardGradient 3. Find the gradient of the following scalar functions. TAPKY (c) f(x,y)= at (-1, 1) (d) (x.y.z)= کے √x² + y² + z²arrow_forward
- Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2) = tan(3), 10 sec-(3), 10 sec-(3)arrow_forwardFind the gradient of the function at the given point. Function Point f(x, у, 2) x² + y? + z? (2, 7, 4) = Vf(2, 7, 4) = Find the maximum value of the directional derivative at the given point.arrow_forward= Calculate the directional derivative of g(x, y, z) z² - xy + 3y² in the direction v = (1, -6,4) at the point P = (2, 1, −3). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(2, 1, -3) =arrow_forward
- Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y2 + z² (2, 7, 9) Vf(2, 7, 9) = Find the maximum value of the directional derivative at the given point. 4arrow_forward3. Let f(x, y) = sin x + sin y. (NOTE: You may use software for any part of this problem.) (a) Plot a contour map of f. (b) Find the gradient Vf. (c) Plot the gradient vector field Vf. (d) Explain how the contour map and the gradient vector field are related. (e) Plot the flow lines of Vf. (f) Explain how the flow lines and the vector field are related. (g) Explain how the flow lines of Vf and the contour map are related.arrow_forwardQ5: al State and prove the theorem of derivative of inverse functions. -1 bl Use the theorem steps in (a) to find df/dx of f(x) = secx. c\ If u = i + j-k, v = 2i+j+ k, w = -i- 2j + 3k are three vectors, find (1) the area of the parallelogram determined by vectors u and v and (2) the volume of the parallelepiped determined by the vectors u, v, and w.arrow_forward
- 2 Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 2, 1) in the direction of the vector i + j. √5 √5 (Use symbolic notation and fractions where needed.) directional derivative:arrow_forwardFind the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy) at the point (1,5). Give your answer as a unit vector. (sin(5) + 5 cos(5))i + cos(15) i 1+ (5 cos (5))² + 10 sin(5) - cos (5) x Invalid notation. syntax incomplete.arrow_forward3-find the gradient of the function v if w=(xy)/z at the point(1,-2,1), find the directional derivative of w in the direction of vector v = 2i + j − 2k, then find the maximum value of the directional derivative.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,