Sll, dxdydz , where T: 0 < x < 1, 0 < y< v1 – x², Vx² + y² < z< /2 – x² – y²

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

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

Q: 2. y(x-y²)dx + x(x++y²)dy = 0

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Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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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: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

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Q: D Find the Valve of K So that the fallowing Where u= (XxXz) V= (YY) inner praduct in an.

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Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: Let f(x,y) = x² – 8x + 2y² + 4y + 7. a. Find and classify all critical points of f.

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Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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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: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

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Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

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Q: the IVP ly a Sum of povers up to and including x5. cx-2) y'= xy, yroje 4 Q.6. Salve pover ceries and…

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Q: Evaluate the porticalar çoution of: y(み-yty)x - x(4-y)dy %=o when x=1, y = 2 A- y?Inx + xy + x* =…

A: y(2x2+y2-xy)dx - x2(2x-y)dy = 0 dydx=y(2x2+y2-xy)x2(2x-y) dydx = (2x-y)xy + y3x2(2x-y) dydx = xyx2 +…

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: Find the general solution of the DE dyldx = y(x – y) /x^2. O y = C/ In(y) O y = C/ In(x) O y = x /…

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Q: Let f (x, y) = x³ + y? – 4xy + 3x + 2y + 5. Find and classify all critical points of f.

A: *concept:- maxima and minima in partial derivatives.

Q: Given: Z WXY = LXZY Prove: (XY)? = WY•ZY

A: Given: In the figure ∠WXY≅∠XZY. To prove: XY2=WY·ZY.

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: Evaluate 3xz dV where E {(x, y, z) | 2 < x < 5, x < y < 2æ, 0 < z < x + 2y}

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Q: X+Z Evaluate f'SS CSIT (*+y+z)dx dy dz. X-Z

A: To evaluate

Q: Let N = {(x.y. z) e R³ : (x² + y^)° + z² < 4, z<1}. The integral / 16 z (x² + y²)' dx dy dz is equal…

A: Given that,Ω=x, y, z∈ℝ3: x2+y28+z2≤4, z≤1∫Ω16zx2+y27dxdydz is evaluated as shown below.

Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

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Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Let T = x²y-xy³ +2; x=rcos0, y=rsin 0. Find and OT at or 20 TAT

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Q: (a) x² + zsen xyz = 0

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Q: Let f (x, y) = r³ + y? – critical points of f . 4xy + 3x + 2y+5. Find and classify all

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Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

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Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: Find dy any ay of Ay of y =f(x) = x² +x at x= 10 when ax =0.1.

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Q: dV where V = dt y- x x= 2t, y = 5t, and z = t. Use the Chain Rule to find x+z' av dx (Type an…

A: Please see the explanation below

Q: H.W: Evaluate the integral: 1. √2 3y 8-x²-y² SS S 0 0 x²+3y² dzdxdy

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Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

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

Q: Display the values of the functions in Exercises 37–48 in two ways:(a) by sketching the surface z =…

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Q: f (x, y, z) = x² + y² + z² and u = (1,0, 1) at P(1, 1, 1).

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: || | /3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8. %3D

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Q: Let f(r,y) r+ 12ry+12y. Find all the critical values and claesify them.

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Q: R Be denned by J (, 9, · Explain why we can always find the maximum and minimum of f(x, y, z) in the…

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Q: xcos y d4, D bounded y =0, y=x and x=1.

A: This is related to integral calculus

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

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Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

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Q: Q.1 The natural domain of fur f(x,y) = lnx² + Iny is а) {(х, у):х > 0, у > 0}

A: Log function is defined for positive values

Q: 3 Find the bounded Solution of : = xt メ>。,t>。 >y(メノ) where y cx, o) = %3D and y co,t) = 0 . Ansi] y=…

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Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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