Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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

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Q: Find the antiderivative for each tunction When C=0. a) g(x)= -3x-4 b) nlx) = x-4 %3D c) Kl) =x42x+3

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Q: Let f(æ, y) axy + az?y+ y³. (a) div(grad(f)) = (b) Find a so that div(grad(f)) = 0 for all æ, y. %3|…

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Q: = Find fus fay, fyx and fy for f(x, y) = e*/y

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Q: (a) D = (x + z)a, (b) E = (y² – x³)a, + xyza, + (x² – z?)a.

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Q: 4 x2 + 4

A: We have to find out the antiderivative

Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

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Q: Let z=xln(x2+y²-e*)-154xy, x=te, y=est. If the value of Oz when s=2 and t=1 is equal to Ae?+Be, then…

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Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: a. Find the antiderivative of f(x) = -25x e F(x) = %3D

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Q: Find the antiderivative for each. function When C =0. レト a nx)= csc²x LSC b) scx) = } csc 2 7X C)…

A: Solve the following

Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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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: Find (∂z)/(∂s) and (∂z)/(∂t), given: (e) z = exs ; x = s2 + 2st, y = 2st + t2

A: Given:To Find (∂z)/(∂s) and (∂z)/(∂t)(e) z = exs  ; x = s2 + 2st, y = 2st + t2

Q: sume that w = and f (x) = e . Find and dt ds II II

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

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Q: f(x, у, 2) dV

A: Given data:     The expression for the given integral is The given function is: f(x,y,z)=e5z. The…

Q: valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

A: F(x,y,z)=(z,x,y)

Q: Evaluate by USing first Substitution and then partial Prachons TF necessary. 3x dx .3x e

A: We have to integrate above function by substitution and then by using partiap fraction Please see…

Q: dydx What is the reversed order of integration of ,3 O a. а. dxdy b. ,9 cvy x²ev°dxdy c. dxdy .3 cvy…

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Q: Evaluate S, y dv with E = {(x, y,z): 0 <x< 3, 0< y < x, (x – y) < z < (x + y)} %3D

A: Use triple integration

Q: Find the ic by using Least cost Method? Di Dz D3 Dy supply 10 20 %3D 15 12 7) 20 2, 25 14 16 18 15…

A: D1 D2 D3 D4 supply S1 10 0 20 11 15 S2 12 7 9 20 25 S3 0 14 16 18 15 Demand 15 15 15 10…

Q: uppose ſ, f (x)dx = 8, f(x)dx = 10 , §' g(x)dx = 4 , fó g(x)dx = %3D %3D %D ind : f (x)dx 4 [f (x) +…

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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

A: Given,

Q: Find /| v'e*** - y? when D={(x,y)E R? | x>0,y>0,x² + y?<1}

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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: Find the antiderivative of g(t) = 2t2 t3+1

A: Topic:- integration

Q: (a) Find the effective noise Temperature Ts of an equivalent resistor with resistance equal to the…

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Q: Evaluate 3xz dV where E = {(r, y, z) | 2 < ¤ < 4, x < y < 2x, 0 < z < x + 2y}

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Q: Let y = uy and z = u + y, where u and y are positive independent variables. a. If u is measured with…

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Q: Evaluate ff, (x - y + 1)dxdy, where R is the region inside the unit square in which x + y = 0.5. |

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Q: For a bivariate analysis involving the two variables X and Y, if E(* – a)(y - 9) = -76, n = 33, S =…

A: It is given that, ∑x-x¯y-y¯ = -76, n = 33 Sx =1.54, Sy =2.40,

Q: What is the value of x in dthe triangle below? 10 B. C. B. Sv2 C. 10v3 D. 20

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Q: Determine all values z ∈ C satisfying  e^z = −2i.

A: ANSWER :

Q: Calculate ffs f(x, Y, z) dS For x? + y? = 16, 0 <z< 7; f(x, y, 2) = e Sls f(x, Y, z) dS 4pi(1-e^-7)

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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: Consider the bivariate function f : ACR? → R : (x, y) → f(x, y) = ln(4x² + 2y – 6), %3D with A =…

A: As per the question we are given the following bivariate function : f(x,y) = ln(4x2 + 2y -6) And we…

Q: Given f(x, y) = – 5x + 6xy° + 3y, find - fa(z, y) = %3D f,(z, y) = !!

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Q: Differentiate W.r.t to x ne*

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Q: e |/ (x² + y³) dV, where E = {(x, y, z) E R³ : VA- x² – y? <z< V9– x² – y?}. Evaluate E

A: The region E will be bounded within the upper half of the spheres x2+y2+z2=(3)2 and x2+y2+z2=(2)2.…

Q: If Sis g(x) dx = -45 and G(18) = -33, where G(x) is an antiderivative of g(x), find G(6) %3D

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Q: Consider the joint pdf fxx (x, y) = cxy, for 0<x<3, 0<y<x a) Determine the value of c. b) Find the…

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Q: Find the most general antiderivative. dy A В c) 8 +C D

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Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: Evaluate x dV E where E = {(x, y, z) E R³ | 0 < z < x+ y,0 <x < y?,0 < y < 1}.

A: Given: Now,                ∫01∫0y2∫0x+yxdzdxdy=∫01∫0y2xx+ydxdy=∫01y52+y63dy=1184

Q: Find ∂z/∂y for z=e^xy

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Q: Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

A: follow next step

Q: Find 2 by using the Chain Rule with y as a composite of dx y = csc(u), u = x3 + 2. %3D

A: Given: y=csc( u) , u=x3+2  To find dydx

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd