I x In y dA, R = [0, 3] × [1, e] 43.

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

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: y"(t) – 4y'(t) + 5y(t) = e"U (t – 2), %3D

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

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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: x=In i y=r2, find y " when For x=0• O 8 O 4 O 16 O 2

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Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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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: D = {(x, y) E R² :0<x <∞, 0 < y<∞} olmak üzere, [ rye--v°dA D.

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

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Q: z= em and a = 2t– 2s?, y = 2s – 2t, find az at t = 1, s = 1. at

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Q: dy Given a DE of dz 1-r-y using simple substitution, what must be your z? Ity Answer:

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Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: "III. Vf dr = , where f = xy²z and Cis given by r (t) = (t +1, t², t³),0<t<2

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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: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

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Q: ∫C  ez / (z - πi) dz where C is defined as z(t) = 2eit and 0 ≤ t ≤ 2π

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Q: 10. What is 2ri 2 fo, h (z) dz?

A: curve C3 encloses points of singularity z=-2 and z=0 in clockwise and counterclockwise directions.…

Q: Ut for 0 <x <l u(x,0) = x u(0, t) = (1, t) = 0

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Q: * Evaluate SSS 12z dV E where E is enclosed z = x² + y? and z = 1 %3D Зл о 2л о 4л о IT O

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Q: (e) The method ди = dx h order 2. [u(x+h),y(t)—u(x,y(t))] is of

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Q: CALCULATE I = 2² + y² + z*dædydz, WHERE "T" IS THE CILINDER 2² + y? < 1,0 < z < 1.

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: 10 dz where C2 is the top half C2 that is C2: |2| = 2 with z = re", 0 < %3D

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Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: Evaluate SSS 2e(a²+y²+z?)"² dV over B where B= {(x,y, z) : x² + y² + z² < 1}. Take n = 3.

A: • The given region B has spherical symmetry, so it will be easy to solve this volume integral in…

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

Q: find dw/dx, dw/dy, dw/dz using implicit differentation. Leave your answer in terms of x,y,z,and w.…

A: To find the implicit differentiation of the function: ln(2x2+y-z5+11w)=z...(1) So, take w as a…

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

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Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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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: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

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Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

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