af af af Find and дх ду Əz f(x, у, z) 7In(x + y + z) af ax af %3D ду af az Find their values at (0, –1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) af -(0, –1, 1) ax = af -(0, -1, 1) ay af -(0, –1, 1) = az

Q: The equations xy? + 5xzcos(u) + ye" = 10 and x³yz + xe" – 3u²v² = 9 are solved for u and v as…

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Q: use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02) given g (x, y, z)…

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Q: 1. On (-1,1), two functions y1(x) = e2ª cos x, y2(x) = e2« sin x are %3D linearly independent…

A: 1.On (-1,1) two functions y1(x)=e2xcosx,y2(x)=e2xsinx 2.On (-1,1) two functions…

Q: 11. f(*, у) — х2- 3ху, г(t) — (сos t, sin t), t - 0 12. f(x, у) — х? - 3ху, г() — (сos t, sin t),…

A: 11)

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Q: af of H.W: Find and for the functions: b əx ду 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2)…

A: Given functions are 1. f(x, y)=(xy-1)2 3. f(x, y)=(x2-1)(y+2) 4. f(x, y)=x(x2+y2)   To Find: ∂f∂x…

Q: af af af Find and 1. дх ду dz f(x, y, z) = 3×EY2 + 7yexz %3D af af %3D ду af az Find their values at…

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Q: gradient field that corresponds to function (x, y, z) = y2 -x2 +x e=2 - y3 z

A: This is the question from Vector Calculus.

Q: f(-1,3) = 4, fr (-1,3) = 5 and fy (-1,3), then the linear approximation to f(-1,3; 3,2) is

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Q: Find the linearization of f(x, y, z) = at the point (3, 2, 8). (Express numbers in exact form. Use…

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Q: .2 .2 .2 Find the linearization L(x,y,z) of the function f(x,y,z)= x+y The linearization of f(x,y,z)…

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Q: A function f(x, y) = x3 − 3xy2 + y3 is homogeneous of degree n when                f (tx, ty) = tnf…

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Q: The equations xcos(u) + 7uy2 + e + 2 = 0 and 2ye" + 4x2v - 3xcos(z) +1 = 0 are solved for u and v as…

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Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: Suppose a function z=f(x,y) has critical points at (-1,2) and (0,3). Furthermore, suppose at each…

A: Let's find.

Q: Ax. 19-22 Compute Ay and dy for the given values of x and dx Then sketch a diagram like Figure 5…

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Q: Axy:z) =xsin(yz) given 1. calculate fy (x,y,z), fy (x,y,z), fz (x,y,z), fxyzxyz (x,y,z) 2. given x =…

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Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

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Q: 1) f(x, y) = y-x. (2,1) Ans. Vf =-i+j 8(x, y) = y-x'. (-1,0) 3) f(x, y,z) = x +y-2z+z In(x), Ans. Vg…

A: Since you have posted multiple subparts question so i have solved first three parts as per our…

Q: C(c1, C2, $1, A1, A2) = u(c1) + u(c2)+ A1 [Y – P;C1 – s1] + A2 [(1+r)s1 – P,c2] . Take the first…

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Q: f(-1,–5)= f(-5,–1)= f(0, 0)= f(5, –5)= f(t, 2t)= f(uu, и — v)-

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Q: The equations xcos(u) + luy² + e² + 2 = 0 and 9ye" + 4x²v – 3xcos(z) +1=0 are solved for u and v as…

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Q: max f(x, y, z) = -xz-x² + y-yz - y² - 3z² x,y,z ...5] Express V f(x, y, z) = 0 in the form Ax = b…

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Q: Let f(x, y) = x+ 2xy − 2x − 4y be a function in x and y, then: a. (2,3) is a critical point b. (−2,…

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Q: Problem : If f(x, y, z) = In(x³ + yl2 + 2) + V(T12 + y+ 2), then find fz, fy and f; at (1, 1, 1).…

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Q: Over the past twenty years an economy's total output has grown from 1000 to 1300, its capital stock…

A: Solution

Q: 8. Let f(x,y,z) = xy² + yz² + zx². The directional derivative of f(x,y,z) at the point P = (-1,1,2)…

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Q: 7. The directional derivative of f(x, y, z) = xe +xye at the point P(-2,1,1) in the direction…

A: The given function is: f(x,y,z)=xeyz+xyez

Q: A function f(x, y) = 2x2 − 5xy is homogeneous of degree n when                      f (tx, ty) = tnf…

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Q: a²u ax² a²u =1- x for 0 0, - u(x, 0) = x²(1 – x) for 0s x s 1, du (x, 0) = 0 for 0 s xs 1, at d" (0,…

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Q: 7. Classify the critical points (0,0) and (+,0) of f(x,y) if fay (0,0) = 0, f (0,0) = -2, fyy (0,0)…

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Q: The equations ry² + 6xzcos(u) + ye" = 12 and x³yz + xe" – 7u²v² = 21 are solved for u and v as…

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Q: Example :- Find the deflection u (x,t) velocity string length L= T, C2=1, its ends fixed if the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The equations æy? + 2xzcos(u) + ye" = 4 and x³yz + xe" – 8u²v² = 24 are solved for u and v as…

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A: Where C is arbitrary constant. Which is the required potential function.

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