Let f(z) = kz5 + az3 + cz.  Find v(x,y) if z = 6.7 + 2.9i , a = 7, c = 11, and k = 5. Round off your final answer to five decimal places.

Q: If f(x, y) = 4e*y cos (x- 1) , then the linear approximation at (1,0) is | (A) 4 + 16x (B) 4 + 4x…

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Q: If z = x - 2y, dz and x = 2t, y = 5t, then the value of dt Select one: True False at t = 3 is equal…

A: Here, the given functions are: z=x-2y,x=2t, y=5t⇒z=(2t)-2(5t)⇒z=2t-10t⇒z=-8t

Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

Q: Let f(z) = az4 + kz3 + bz2.  Find u(x,y) if z = 5.7 + 2.2i , a = 9, b = 10, and k = 8. Round off…

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Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

A: Given: x2+3y2=c and Px,y=1,2   Now differentiate the given function with respect to x.…

Q: Find ∂ w/∂ x at the point (x, y, z) = (2, -1, 1) if w = x2 + y2 + z2, z3 - xy + yz + y3 = 1, and x…

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Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: If g(x) == [e'-In(2t+1)]dt, find g''(x) . dx A ex-In(2x+1) 4 B (2x+1)² 4 (2x + 1)² 2 D (2x + 1)²

A: Here given that: g(x)=ddx∫-1xet-ln(2t-1)dt Using the Fundamental Theorem of Calculus: g(x)=ex-ln…

Q: If f(x,y,z) = e2x+3y-4z + xyz And x = 3si n(rt) y = 2cos(rt) z = r² + t² af Find at

A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: If z = f(x, y), where f is differentiable, and g(t) g(3) = 2 g'(3) = -3 fx(2, -8) = 9 X = h(t) y…

A: Given,           z=fx,y, where f is differentiable, and                x=gt    and    y=ht…

Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

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Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: For the family x² + 3y² = c, find that member of the orthogonal trajectories which passes through…

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Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

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Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

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Q: f(x, y, z) = 3x + 2y + 4z, x2 + 2y2 + 6z2 = 21

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Q: Let f(z) = kz5 + az3 + cz.  Find u(x,y) if z = 3.9 + 6.3i , a = 5, c = 10, and k = 4. Round off…

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Q: Let f(z) = kz5 + az + cz. Find v(x,y) if z = 6.3 + 3.3i, a = 8, c = 12, andk = 5. Round off vour…

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Q: If f(x,y) = 3e2y cos (x-2), then the linear approximation at (2,0) is %3D (A) 3-3x (B) 3+ 6y (C)…

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Q: f(x, d,Z)cbxcly dz

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Q: 2: Find the orthogonal trajectories of xy=C.

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Q: Let  z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal…

A: z=xlnx2+y2-e4-176xy x=tes,     y=est use the chain rule to find the partial derivative…

Q: If f(x, y) = 3e-2x cos (y – 2), then the linear approximation at (0, 2) is (A) 3 – 3x (B) 3+ 6y (C)…

A: A function of 2 variables can be linearized using the partial derivatives. The formula for the…

Q: Let f(z) = az4 + kz3 + bz?. Find v(x,y) if z = 2.9 + %3D 7.9i , a = 19, b = 16, and k = 3. Round off…

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(4) = – 4, g'(4) = 9,…

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Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: 1. Let T1,T2 : R3 → R² be given by: T1((x, y, z)) = (3x – 2y + 5z, x + 4y – 7z), and T2((x, y, z)) =…

A: Solution is given by using the matrix representation of given transformation as

Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: Let w = x2 + xy + z2.(a) If x3 + x = 3t, y4 + y = 4t, z5 + z = 5t, find dw/dt.(b) If y3 + xy = 1 and…

A: Answer(a): Given that, w = x2 + xy + z2 and x3 + x = 3t, y4 + y = 4t, z5 + z = 5t . Now,…

Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

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Q: Let f(z) = 5z2 + 4z.  Find u(x,y) if z = 9.6 + 2.9i .

A: Using , complex function properties

Q: Let f(z) = az4 + kz3 + bz2.  Find u(x,y) if z = 6.2 + 2.4i , a = 6, b = 18, and k = 3. Round off…

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Q: Q3: 1f f(x, y) = 4xCy5 + 6x*y* .Prove that: f(x,y) * fxxyy fxx * fyy = 1

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Q: The orthogonal trajectories of y = 9ax is where a is an arbitrary constant y + = 4c 2 Oy +x2 = 9 O…

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Q: Suppose that , g(t) dt = v2 g(r) dr V2 b [-g(x)] dx а. -3

A: Given: ∫-30g(t)dt=2. The objective is to find, ∫-30-g(x)dx ∫-30g(r)dr2

Q: If f(x,y,z) = 3zx²eY , grad f = Select one: 2 у 2 у a. 6ze'i+ 3zx e'j+ 3zx e’k y 2 у b. O b. 6zxeYi+…

A: We are given f=3zx2ey to find the grad f

Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal to…

A: we have to partial derivative by using chain rule

Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

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Q: Let f(x,y,z)=x^3 yz^2+4xy^2 z+y^2 z-2y^4 z^3 find fxyz

A: Use the following formulae, to obtain the solution.…

Q: Let f(x, y, z) = 3x?y+ yz3, where x = 3 – t2, y = 2t + t3, and z = V1+ 3t. Calculate when t = 1.

A: NOTE: Refresh your page if you can't see any equations. . here we have . the given function is…

Q: (b) Compute f er+uds, where c(t) = (t, 2t), t e [1, 2]. %3D

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Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Q: If z = u2 v3 w4 , u = t2 , v = 5t − 8 and w = t3 + t, find dz/dt

A: Given,           z = u2v3w4 , u = t2 , v = 5t − 8 and w = t3 + t

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

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