5) Put f(x,y) = e-(*). Find Vf at an arbitrary point where x = 0, and...
→ (1 point) Let Vf-6xe-r sin(5y) +1 5e* cos(Sy) j. Find the change inf between (0,0) and (1, n/2) in two ways. (a) First, find the change by computing the line integral c Vf di, where C is a curve connecting (0,0) and (1, π/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 t 1, K) = dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily...
(1 point) Let Vf =-8xe-r sin(5y) 20e-x. cos(Sy) j. Find the change inf between (0,0) and (1, π/2) in two ways vf . dr, where C is a curve connecting (0,0) and (1.d2). (a) First, find the change by computing the line integral The simplest curve is the line segment joining these points. Parameterize it: with 03t s 1, r(t)- so that Icvf . di- Note that this isn't a very pleasant integral to evaluate by hand (though we could...
Find Vf at the given point. f(x,y,z)=e*** cos z + (y + 2) sinx (Type an exact answer, using radicals as needed.)
please answer asap (it is all the professor asked) (5) Consider the gradient vector field F ▽f where f(x,y) = cos(2x-3y). Find curves G and C2 that are not closed such that JG F·dr = 0 and 1, F . dr-1. Explain why you pick the curve you do, and how you know the integrals have the correct values. (Hint: Try picking a straight line between the origin and some simple point (a, b) that you choose later.) (5) Consider...
2. Let f(x, y) = xy (2] (a) Findäf af and Vf. 5 (b) Find a unit vector u for which Duf(v2, V2) = 0. 2. Let f(x, y) = xy (2] (a) Findäf af and Vf. 5 (b) Find a unit vector u for which Duf(v2, V2) = 0.
2.1(9pts) Consider thc following contour plot for thc arbitrary function f(x,y): Y 0 2 Х -1 + 1. What is vf(0,0). Why? 2. At the point (0,2), in what direction should one move to increase the fastest? 3. Which vector has the greater magnitude: Vf(-1,0) or f(2,0)? CS Scanned with CamScanner
Find Vf at the given point. f(x,y,z) = x3 + y3 – 322 + z Inx, (1,5,5) Vf|(1,5,5) = Di+(\)j + ()k (Simplify your answers.)
Find Vf at the given point. f(x,y,z) = x2 + y3 – 322 + z Inx, (1,1,4) Vf|(1,1,4) = i+ )j + (O)k (Simplify your answers.)
Example A.3 Surface normal vector. Let S be a surface that is represented by f(x, y, z) -c, where f is defined and differentiable in a space. Then, let C be a curve on S through a point P-Go, yo,Zo) on S, where C is represented by rt)[x(t), y(t), z(t)] with r(to) -[xo. Vo, zol. Since C lies on S, r(t) must satisfy f(x, y. z)-c, or f(x(t), y(t), z(t))-c. Show that vf is orthogonal to any tangent vector r'(t)...
2. Let if r and y are not both 0 f(x, y) = 0 if (x, y) = (0,0) (a) Show that and we both exist at the origin are are zero (b) Let v = (v1, v2) be a unit vector with vị and v2 both not zero. Prove that V (f) at the origin exists, and compute it directly from the definition. Does the formula Vu(f) = (Vf). ✓ hold at the origin? (c) Is f differentiable at...