9. Given countour map of = {(2,y), sketch the gradient vectors (with approximate length and direction):...
5.
3. State the magnitude and direction of each of the vectors given below. a) r--30 m (displacement vector) b) v 60 m/s west (velocity vector) c) F 20 N at-45° (force vector) d) p50 kg m/s at 25° (linear momentum vector) 4. Provide a graphical example of a 1-dimensional vector (ID) and one of a 2- dimensional vector (2D). Be sure to include reference axes with labels in each case. 5. 1D Vectors. Let vector A +3 units and...
3.
3. State the magnitude and direction of each of the vectors given below. a) r-30 m (displacement vector) b) v 60 m/s west (velocity vector) c) F-20N at-45° (force vector) d) p50 kg /s at 25° (linear momentum vector) 4. Provide a graphical example of a 1-dimensional vector (ID) and one of a 2- dimensional vector (2D). Be sure to include reference axes with labels in each case. 5. 1D Vectors. Let vector A +3 units and let vector...
1. (a) Sketch a contour diagram for the function (x,y) y, and include gradient vectors at some various points. (b) Sketch a contour diagram for a function g(z,y), and include some gradient vectors, where the following propertics are satisfied The gradient vectors at points on the r-axis (other than the origin) are all parallel but never equal. In other words, for cach pair of distinct non-zero numbers ,2 there's some constant kメ1 such that ▽g(zi,0-k (Vg(T2,0). Vo(x,0)-Vg(r, 1) for all...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g represents the direction in which g increases the fastest. Notice that this is the direction in the xy plane corresponding to the steepest slope up the surface, with magnitude equal to the slope in that direction. 1. At the point (2, π), find the gradient, and explain what it means. 2. Use it to construct a vector in the tangent...
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy-- dx (a) y(-2) = 1 (ь) у(3) - 0 (c) y(0) 2 (d) y(0) 0
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy-- dx
(a) y(-2) = 1
(ь) у(3) - 0
(c) y(0) 2
(d) y(0) 0
Section 15.1 Worksheet Find the gradient field F = νφ for the potential function φ. Sketch a few level curves of φ and a few vectors of F. φ(x, y)-yx2+ y2 for x2 + y2 2. 9, (x, y) # (0,0)
Section 15.1 Worksheet Find the gradient field F = νφ for the potential function φ. Sketch a few level curves of φ and a few vectors of F. φ(x, y)-yx2+ y2 for x2 + y2 2. 9, (x, y)...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
Solve the following problems. Show your work clearly. Q1. (10+10+5=25 points) a) Find the gradient of the function f(x, y) = 3x2 – 2xy + 2y and calculate it at (-1,1). b) Calculate the directional derivative of f(x,y) = 3x2 - 2xy + 2y at the point (-1,1) in the direction of the vector v =< -2,2> c) After solving part (a), if the vector in part (b) was given as v =< 1,0 > could you find the derivative...
how do you do 7 and 8 ?
ah arbnrary number nents, and all 2-companents separately to f of vector ately to find x-, y"r z-components of the resultant vector. B) Break the (given) vectors down into their x-, y, and 2-componerto c) Combine total x, y-, and z-components using Pythagorean Thetee sine the resultant vector and use tangent to determine its angle. and cosines nd the magnitude of Graphical Representation of Vectors You will need o ruler, graph poper,...