Let F = (yey, xey) and let C be given by: x = sin(t), y et-¹ (1- = cos(πt)), 0≤ t ≤ 1. Show that is conservative and find a potential function f. Evaluate F. dr using Theorem 2.

Q: et Evaluate the derivative: da 4 S (3t2 – 2t + 4) dæ.

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Q: Let F (r, y, z) = sin y i+r cos yj- sin z k.

A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

A: Our objective is given below:

Q: Q2] Find the analytic function F(z) if u = coshy.cosx, (B.C. v-0 at x=0)

A: at

Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: Find the directional derivative of f(x, y, z)= = in the direction from P to Q(2, 4, -1). NOTE: Enter…

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Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: 87; Let flxiy,2) =% Cos(Tx) + kon (s2). Then find the directional derivative of f the point…

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Q: Let f = -2x² + 5y² where x cos(t) and y = sin(t). af Ət using the chain rule. Write your answer as a…

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Q: Find the directional derivative of J(, 9) + 3y at the point (2, the direction 57 radians.

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Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: Evaluate this function of z = cos x sin y; x = u – v, y= u² + v². Use chain - dz rule to find ди А.…

A: The given function are z=cosx siny; x=u-v, y=u2+v2.   Rewrite the given the function as follows.…

Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

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Q: f(t) = mt + b+ A sin-

A: Given data:     The given price of the model is: f(t)=mt+b+Asin(πt/6). The given price on the first…

Q: = Evaluate and at the point (7, 7, «) using the implicit relation sin(z + y) + sin(y + z) + sin(z +…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: one of the following pairs of functions are orthogonal on interval [-1, 1] Select one: x.cosx b. x,X…

A: Given the interval [-π,π] and the pair of function. a. x2,cosxb. x,x c. sinx,xd. NOTe. sinx,cosx We…