1. [ F · dŘ, where F(x, y) = xy î + 3y² ĵ and C : Ř(t) = t² î + 2t ĵ, 0 ≤ t ≤ 1 S F. dR, where F(x, y, z) = y î − x ĵ + z k and C : R(t) = (sint, cost, 2t), 0 ≤ t ≤ π

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fxy.

A: Given:  Let fx, y=xy+x+x cos y To Find:  To determine fxy.

Q: Find V × (V × F) if F(r, y, z) = xyj+ 6xyz k.

A:

Q: 1. The temperature at the point (r, y) on an unevenly heated plate is given by T = f(r, y) = 100+…

A: Given f=100+5x2+15x+10y2gradient of f∇f=∂f∂xi+∂f∂yj     =10x+15i+20yjAt (2, 1)∇f=10x+15i+20yj…

Q: Cives とz f(xy)= J36-9メ-す i) Find domajn and Ram ge Foy the fuclien

A:

Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

A:

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: * (b) Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t I, is a…

A: 6)b) Given  that :         Then, [velocity  of  the object]             and [acceleration  of the…

Q: Let r be the function defined by r(t) = (/10sen t,t, /10 cos t) where the coordinates of r(t) are…

A:

Q: Use the definition of differentiability to show that f(x, y) = y² – xy+5x is differentiable…

A:

Q: Assume that f is a de ferentiable function with fax (5,0) =6 and fu(5, )=4. Let w Cu,v) =f (x (u,v),…

A: Given,w(u,v)=fxu,v,yu,vx=6 cos u+5 sin vy=7 cos u sin vfx(5,0)=6 and fy(5,0)=4 To find:wuπ2,π2

Q: u(x, y) = e¯ª (cos x cos y cosh y - sin x sin y sinh y)

A: We have to find the analytic function for which the real part is u(x,y)=e-x(cosx cosy coshy-sinx…

Q: Use the linear approximation of f (x, y, z) = √/5x² − 3y² – xy + 5z³ at the point (-2, 1, 1) to…

A: Use taylor approximation of first order

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

A:

Q: Let f (x, y, z) = xyz. Determine the value of fryy + fyay – 2 fyyr Simplify your answers.

A: We have to find the value.

Q: 0, x? < y < 2x² 1, otherwise. Show that f.(0, 0) and f (0, 0) exist, but ƒ is not differentiable at…

A:

Q: Let f(x, y) = 2x² + 4y² + 2xy+ 10x + 3y + 9 Find D = frr · fyy - i

A:

Q: 1. Let f(u, v) be a continuously differentiable function. Let u = e*, v = e³. Show that u²fuu + v²…

A: Given that f(u,v) is a continuously differentiable function, and u=ex, v=ey then show that…

Q: Let F(x,y,z) = (y,x²,zy) where C:R(t) = (cost,sin t , 3t) and t e [0,2]. Evaluate %3D %3D •dR

A: We have to find value of given Integral.

Q: Evaluate O A. OB. O C. O D. -2 (2) (1) -² (+-) 2 - dt at t = for the function w(x,y,z)=- 4 9 xy ()…

A:

Q: 1. For the function f(x, y) = In root (2 + xy), find the equation of the tangent plane at the point…

A: Note: As per the guidelines we are supposed to answer only one question because this is not a…

Q: Consider the 2D domain D = (x, y)|y > 0, ; < x² + y² < x 1. 1 d(x, y) using / / Calculate dr d0 set…

A: