Find all the first order partial derivatives for the following function. - (sin xy)cos yz 2) flx ,y, z) y 009 )lcosyain xy)lein ) Co2lyz sin ky/sin 2) df COS Cos 2y2 cos yos v2 - 2lyz in xy)lain y?) ах d. af ах
Evaluate the following: where S-( (z, y) є R2 : 0 ST/2,0 < y ST/2). (a) Jls (cosz-s (b) fdl where y is the line segment from (2,-1,3) to (0, 1, 4) and f (x,y,z)-y+2 sin y) dA 3 marks 3 marks (c) Jc F dr where C is the unit circle centred at the origin, traversed once anticlockwise and F R2R2 is given by F(r,y)- (x2.x + y) 3 marks JJR eVEdA where R is the region enclosed by...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
3)If w = x2 + y2 + z2 ; x = cos st, y = sin st , z = sat find 4)Find the minimum of the function f(x,y) = x2 + y2 subject to the constraint g(x, y) = xy - 3 = 0 5)Find the first and second order Taylor polynomials to the function f(x,y) = ex+y at (0,0). 6) Let f(x, y, z) = x2 – 3xy + 2z, find Vf and Curl(f)
1.) Let f(x, y, z) = xy?z3 – sin(xy) +erz? – tan(y, 3. Determine the following. (a) e (b) (c) azonos
(10 points) Find all first and second partial derivatives of f(x,y) = 24 – 3.z”y2 + y* [Note: By Theorem 13.3 on page 913 of the textbook, it should be that fry = fyr:]
Find partial differential z/partial differential x and partial differential z/partial differential y if z^2 +zx sin(xy)+ x^3y = 0 Find partial differential f/partial differential u, evaluated at the point where u = -1 and v= 1, if f(x, y) = x^3y, x(u, v) = v - u, and y(u, v) = u^2 +v^2
3. (a) Find the partial derivatives (with respect to r and s) using the chain rule:[express the final answer in r and s only ,y= r2 +In(s) and z-2r wx2y +z2 ; where x (b) Find dt if f (x, y) = xy + z; where x cos t ,y = sint and z = 3t2
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.