Evaluate В: А: 3e-422 dz Jye-y dy 0, 0,

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

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Q: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: . (4fy – 152 – y) dt + (tª + 3y² – t) dy = 0

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Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: dy Find da if y = In(xiV1+ z° dy %3D dx

A: Recall: d(u.v)dx= u dvdx+dudx v d(xn)dx= n xn-1 d(ln x)dx=1x

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

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Q: Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

A: We have to find the definite integral using substitution method In place y^2 =t                2y dy…

Q: Calculate fls f(æ, y, z) dS For 2² + y² = 16, 0 < z S ls f(x, y, z) dS =

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: Evaluate II elx²+y²+z²) dV where E is the solid inside x² + y + z? = 4 and above z = V3x2 + 3 y² E

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Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: Differentiate. R(t) = (t + et)(4 - Vt) -Vī + 2(4– Vī)(1+e') R'(t) 2t

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Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: y = 2t + Vt dt J4 y' =

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Q: 3- show that the diff. equ. is homogeneous and Salve it (2x +34) dx +(y-x)dy = a

A: In this question we have to solve the differential equation.

Q: Integrate the following using substitution 1) z5 (9z6 – 7)8 dz 2) S dy 4 y3 2-5y4

A: Given that: 1. ∫z5(9z6-7)8dz   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: d'y dy 4+y =r²-21 +3 dt? dt

A: We will calculate CF and PI separately then we will add them.

Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: IL Evaluate (x + y – 3z) dV where E = {(x, y, z) | - 7< y< 0,0 < a < y, 0 < z < x + y?}

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Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y. How is dV/dt…

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Q: Evaluate 3rz dV where E = {(x,y, z) | 2 <r < 5, a <y < 2r, 0 < z< +3y}. %3D Round your answer to…

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Q: (i) J. dt 6. –t²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Evaluate S S12zdV E where E is the solid enclosed by z = 1 and z = x² + y² 2. Immmmm

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Q: dy =r-ky, y(0) = y, dt

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Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: Find y Ly imelicit differen -tiation, VスナUゾ 21

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Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

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Q: what is the Folution when i =0 and t= o ? di + Ri = Esin 2t %3D dt

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Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: By algebraic substitution, the integral dx dx is converted to: 4+Vx dy y+4 2 dy y+4 ydy y+4 2ydy y+4

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: Sv? – 1),/y dy

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

A: Given, u= ∫dx/(4+√x) We can solve it by substitution method.

Q: Differentiate. R(t) = (t + e)(2 - VE) %3D R'(t) =

A: Given function is Differentiating both sides with respect to x by using product rule of…

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: dx dy. Evaluate by changing the order 4y

A: In the given question we have to evaluate the integration                ∫01∫4yyex2dxdy by the…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.