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Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: (a) Si = {(x,y) | y divides x} (b) S2 = {(x, y) | x + y is odd} (c) S3 = {(x, y) | xy is odd}

A: List the properties of relations. Reflexive: a relation R on a set A is reflexive if a,a∈R for all…

Q: 10. Differentiate y = xV A. y = xV (n) 2+In 2 va B. y' = xv (* + C. y' = x* (+ D. y-x" (프+ Im) E.…

A: We need to find differentiation.

Q: oS% (x? + y? + z*) dz dy dy

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Q: 327. F(x, y, z) = zi+ xj+ yk; S is hemisphere z = (a² – x? – y?)/2. -

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Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: Her xG N isin x|x dir ve EN *ly re y/2 ie x|7 dir. dir xly ue ylx ie x=y dir.

A: For natural numbers x and y, x|y then y=ax, where a is natural number

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: D = {(r, y) : 1 <Ise, 0<yS In(r)}

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Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: 1 Evaluate dz, where (i) C is z+ = 2 .2 +1 C

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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: Calculate fryr if Ar.y,z) = &r-9*y³-z³. OA foe =-322 OB fye =0 OC None of these OD fye = 3r2-3y2-322…

A: We have to find the partial differentiation of the function with respect to X y and z

Q: 2.rydr + (z² – 1) dy = 0 O zy? - y = C O zy+y=C O zy - y² + C = 0 Oy-

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Q: dz where c is |z=1 z'e? Evaluate

A: ∮ f(z) dz = 0 when no any singularity lies within region of integration. But if any singularity lies…

Q: ン Frnd in side r=2 inford quarler aren aul sde r= 1+s6

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Q: Let cov(X,Y) = var(X) = and h(y) = }* (4y, 0<y<1 %D %3D 45 45 elsewhere Then the value of var(2X +…

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Q: r In y dr, where D is described by 1 < r < 2, e <y<e aD | V1 +r² dy, where D is described by -1<r<1,…

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Q: "x is between c and d" translates to csxsd O True O False

A: Given query is to find statement is true or false.

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

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Q: dy The appropriate substitution to solve da + In(z + 1)! = x°y3 is O z = y? O y = vr O z = y* O z= y…

A: Topic:-  differential equation

Q: If y = In(x – y) then y' at the polnt where y = 0 Is equal to Select one: b. 2 C. -2 d.=

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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: 6. SS dV に lies b/w ミ 25 %3D and x? f y? + z? Ź 36 in the firót oct ant ...

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Q: . If U = z sin y/x where x= 3r2 + 2s, y= 4r – 2s², z = 2r? – 3s², find a) Or b)

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Q: EX. Use Euler's method (modified) to approx; mad e y' = x+y for yC1) = 1; h=o.1,15X<2 心ふ 14 withe…

A: We have to use modified Euler method to find solution.

Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

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Q: az dz Let z = ex*y ,x = Vuv, y = 1/v. Find = Vuv,y = 1/p. Find ди av

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If y = e3+, x = 0 when z = 1, z=1 z=1 = 3, then what is z=1? dy |3D O 1 O 3 O 21e4 O e30 O 19e30

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Q: -号。 - 4X u (x,o) =3 e 2 , ニ0 y2 Ansl ux,y) = 34(メ+) Ans.l ucx,y) 3 e %3D

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Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: Q/ If the joint p.d.fof X and Y as f(x,y) = }*y (cx?y ,x2sys1 ,0. W find the value of c and P(x 2…

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Q: ind if f(x,y) = y sin xy ax

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Q: Let y(x) be the solution for the DE : y = (x + y – 1)² If y(0) = 1, then find y() %3D %3D 4 37 8- 7…

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Q: If f (x, y) = x² y² – xy³ then find ²f at (1,0). дудх O 1 O -1 O None

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Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: 7 2 dx dy y? 3 Evaluate the integral: Jo 98 3 294 3 196 392 3.

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Q: az az Q1/ a. Find and if z= (x² + y²) where x =r+ e*and ar as y=Ins

A: Solution: The objective is to find the partial derivatives of the given equation

Q: 4. Given (f(x, y) = tan (y/x)), then af 1ay is equal (c) x +y" 1/x (d) x' + y ja) x +y? x +y

A: Some of the formulas of the derivative are ddxtan-1x=11+x2 ddxaf(x)=addxf(x) The partial…

Q: 11. f (x, y) = ery subject to a? + y? = 16 %3D

A: The objective is to find the lagrangian multipliers for fx,y=e2xy subject to gx,y=x2+y2-16. To solve…

Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: R = {(x,y) E R ×x R : x > y} T = {(x, y) E R × R : x > y}. RoT.

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Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

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Q: (a) z, and z4 where z = sin(2x) + y, x = s² – t², and y = s² + t² (b) z, and z4 where z = e*+y, x =…

A: We need to find the partial derivatives z.

Q: 17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D

A: Let h(x, y, z)=x2+y2+z2-z. We now have ∇f(x, y, z)=(1, 0, 0) and ∇h(x, y, z)=(2x, 2y, 2z-1). Let λ…

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer