Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

Q: 3tan z sec? x dr 2.

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Q: 4. dr/dt = -2tr, r(0) = ro %3D

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2

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Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: Find high order DE 6. (D4-5D² - 36)y = 0

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Q: from y = ae + be %3D 2.

A: y=ae4x+be-4x ....(1) Differentiate both side w.r.t x dydx=4ae4x-be-4x        ....(2) From (1) and…

Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

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A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: compute ∫_D 2ydx+3xdy, where D is described by 0≤x≤1, 0≤y≤1

A: Green's Theorem: Let C be a positive oriented, smooth, simple closed curve. Let D be the region…

Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

Q: Find curl(Sz i+6x j + 7y k), curl(Sz i+ 6x j + 7y k) =( i+(

A: This question van be solved using the concept of curl F.

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Q.6 Show that: X-1 X+ y – 1(x-1y)= B(x,y)

A: In the given problem we have to show that                                 x-1x+y-1β(x-1,y)=β(x,y)

Q: Right AXYZ with mZX XY = 12V2 Given: 45° and Find: XZ and YZ

A: Given a right angle triangle ∆XYZ and m∠X=45° and the adjacent length XY=122. To find XZ and YZ.

Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: Compute (T2 T)(x, y). T(x, y) (3x, 7y), T2(x, y) = (x-y, x + y)

A: We have to find T2 composition T1 .

Q: ス+)V2x+x dxメ

A: Given,          ∫x+12x+x2dx

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Q: y show that = 0. . If z: x² + y² II

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Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

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

A: we have to triple integrate using the given limits

Q: Q4- Given y = u2-1 and u = Vx2 +2 find y u2+1

A: Consider the equation On finding the derivative with respect to u

Q: max z = 2x + 8y %3D s.t 3x + 9y 12 х, у > 0

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Q: Suppose that W (y1, Y2) (t) = 4, and y3 Yı – 3y2. What is W (y1, Y3) (t)?

A: Correct option -12 We have to find out the value for Wy1,y3t.

Q: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = -3x2y3 + x3y

A: Given that, fx,y=-3x2y3+x3y Then we get,…

Q: Q5/ find y', y=In(Inx) * O y'= 1/( x-2x)*(2x)=1 O y = 1/( x-2x)*(2x)=2 none of the above

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Q: Evaluate (x - 4y + z) ds. S: z = 5y, 0 s x s 4, 0 sysx

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Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = ( i Di + ( i Oj + ( )k

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Q: If z = (2x + 3y)³ and x = r2 - 2s and y = 2s - r, then when r = 2 and s = 1 is as %3D %3D

A: To find the partial derivative when r=2, s=1.

Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: Compute ƒxxx and ƒxxy for ƒ(x, y) = x3y.

A: Given function - f(x, y) = x3yConcept - While partially differentiating with respect to x, other…

Q: Find the domain of y = vx+6. %3D 12. O x 2 6 O x > 6 1/6

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Find for z = for z = ex-y Əz Əx

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: ди Ifu=r(x* +2yz,y* +2zx)Prove that (y -zx) +(x² - 3z) + (:* - xy) ZX

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Q: y'=xsin^2y

A: Given                y,=xsin2(y) we will solve this differential equation very easily by…

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: Calculate ∂ω/∂z for ω=e -2xe((z^2)y)

A: While calculating partial derivative ∂ω/∂z, all other variable except z will be considered as…

Q: a) Evaluate ²₁ √√1-x² √√1-x²-y²e-3(x²+y²+z²)² dz dydx

A: The given problem is to evaluate the given triple integral of Cartesian coordinates.

Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: əz əz +y show that x 3z x²y2 B. If z əx ду %| x+y’

A: B). From the given function: z=x2y2x+y And x∂z∂x+y∂z∂y=3z As we know that the Quotient rule:…

Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: Compute Δy/ Δx for the interval [2,4] where y = 5x−7.

A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

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Q: Eliminate the arbitrary conutantu 2. %3D y= ax + be

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