Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

Q: Let f € L'(0,1). Assume that f(t)t2"dt = 0 for all n f = 0 a.e. 1,2,3,.... Prove that %3D

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Q: Let f(x, y) = In( + 2y² – xy). Find fæz, fyy, fzy, fya. Confirm that fry = fya.

A: Given: f(x, y)=lnx2+2y2-xy. To find: fxx, fyy, fxy, fyx.  And to show that fxy=fyx. Differentiate…

Q: Let f(x, y, z) = In(x² + 2) + y²e== – cos(2yz). Find fzyz- %3D

A: Given that: f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: Let f(x, y,z) = x² sin y + y e², where x =t + 3,y = net-1 and z = In 2t. dL at t = 1 is: 1-2n O -12n…

A: Given, fx,y,z=x2siny+yez, where x=t+3,y=πet-1 and z=ln 2t.   The objective is to determine dfdt at…

Q: Let f(x, y,z) = x² sin y +y e, where x t +3,y = net-1 and z = In 2t. %3D at t = 1 is: dt O -12n O…

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Q: Show that the two linearly independent solutions of xy" – y + xy = 0, x > 0 can %3D be obtained as…

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Q: Suppose that z = xy² and x and y are differentiable functions of t with x = 1, y = −1, dx/dt = −2,…

A: Given  z=xy2 Also at t=-1 x=1y=-1dxdt=-2dydt=3

Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

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Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

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Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

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Q: Let f(x, y, z) = x² sin y + y e², where x = t + 3,y = net-1 and z In 2t. %3D df at t 1 is: dt %3D…

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Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: Find a linearization L(x, y, z) of f(x, y, z) = x²y + 4z at (1,-1,2).

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Q: Find the value of dr/dt at t = 0 if r = (u2 + 7)^(1/3) and u^2t + u = 1.

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Q: Show that the opelator Tilol defined by Y=19;)=Tx.-E] *=(h:)is Linear and bounded

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Q: Let H(x) integral ,for -2 ≤ x ≤2.Use geometry to evaluate H(2).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

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Q: Let f(x, y, z) = In(x² + z) + y²e®%. Find fzym. Zyx•

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Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

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Q: 2. Show that the function g defined by VVT y² + √² 2, is not continuous at (0,0). (z,y) = (0,0)…

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Q: Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1

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Q: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).

A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)

Q: Compute the first-order central difference approximations ofO(h^4) of t function of y at x = 1h =…

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Q: If f(x, y, z) = In(x7 + yº + z®) + (x° + yº + z®), then find fr, fy and fz at (1, 1, 1).

A: →fx=∂f∂x, During derivative of ∂f∂x, consider 'y' and 'z' as a constant→fy=∂f∂y, During derivative…

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

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Q: Let f(x, y) = xcosy- y'e*y. fxy at (1,0)is equal to: %3D -2/3 -2 1 0.

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Q: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

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Q: Let F(x,y,z) = z* + x+ y sin x + x In z 0, where z fx.y), then at (0,0,1) and are dy equal to: ax

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Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) with f-(1024, 256) = 4 an dz…

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Q: ) Consider the function f(r) = f(1) has a critical number A %3D f"(A) = Thus we conclude that f(x)…

A: Critical point f(x) is the number at which first derivative is zero.…

Q: 2. Let z = sin(xy) + x siny,x=u² + w² and y = uw. 2a. Compute Vz= when u = 0 and w = 1.

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Q: Suppose that z = f(x, y) is differentiable at the point (64, 1024) withf, (64, 1024) = 3 and dz…

A: Topic:- partial derivative

Q: Let f(x,y,z) = x² sin y + y e, where x = t +3,y = net-1 and z In 2t. %3D %3D at t 1 is: dt -2 O None…

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Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·

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Q: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: Use the fundamental theorem of calculus for path integrals to evaluate f.(yz2, xz2, 2.xyz). dr where…

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Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

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Q: Evaluate f(x, y, z) ds. Js f(x, y, z) = x2 + y2 + z2 S: x + y = 36, 0 SxS 6, OszS X %3D !3!

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Q: Use Green's theorem to evaluate f (x²y) dx + y²dy here C is close path formed y = x and y = x³ from…

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Q: Let f(x) = e2sinx 1. Use the local linear approximation of fat x = 0 to approximate e2sin (0.01)

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