+y 5. For the function f(x, y, z) = x cos(y + xz), find fazyz. (7 Pts) 6 Find annuntian ful
5. Consider the function z) = x(T-x). Find the deflection u(z, y,t) of thesquare m em brane of side T and c2 ะไ for initial velocity 0 and initial deflection /(z,y) = F(x)F(v). 5. Consider the function z) = x(T-x). Find the deflection u(z, y,t) of thesquare m em brane of side T and c2 ะไ for initial velocity 0 and initial deflection /(z,y) = F(x)F(v).
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
5. Consider the function z) = x(T-x). Find the deflection u(z, y,t) of thesquare m em brane of side T and c2 ะไ for initial velocity 0 and initial deflection /(z,y) = F(x)F(v).
Part A is wrong and I need help Entered Answer Preview [le^t)/y]+5*cos(5*t)*([-x/(y^2)]+(1/2))+[(6*y/(z^2)]* sin(6*t) 5 +5.2015) (+)+ sino 0.916666666666667 11 12 (1 point) x Suppose w = + where у x = e', y = 2 + sin(5t), and z = 2 + cos(6t). Nie A) Use the chain rule to find was a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e as x. dw dt...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn (a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...