Let X = y = z = and Find r and s so that (а) z %3D 2х, (b) u = y, (с) z+ u %3D х.

Q: Find the most general antiderivative. O se3x + 9eX + c 3 e 3x + 9eX +C Z3x - 9e* + C 7 e 1 3x ex. +

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Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

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Q: Given: WX 1 XZ, YZ 1 ZX, WZ = YX Prove: ΔWZX ΔΥXΖ Y W

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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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: ÖRNEK : y = x° eğrisi, y = 1, y = 8 doğruları sınırlanan bölgenin alanını bulunuz. ve Oy- ekseni…

A: The graph is, Find the area enclosed by the points (0,1), (1,1), (2,8), (0,8)

Q: If w= Xze' y=va²–x² , z=Sirx, then ( dw is

A: we will derivative by using chain rule

Q: Given: z = x3 + xy", æ = uv + w°, y = u + ve" az when u = 3, v = – 2, w = 0 Find

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Q: If f(x,y,z) = e2x+3y-4z + xyz And x = 3si n(rt) y = 2cos(rt) z = r² + t² af Find at

A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: Let h(y,z)=y(e)^−z. Calculate ∂h/∂y and ∂h/∂z.

A: Given : hy,z = ye-z

Q: Compute Δy and dy for the given values of x and  dx = Δx. y = x2 − 5x,  x = 4,  Δx = 0.5 Δy  =…

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Q: ck that y(x) = e rx with r satisfying ar 2

A: Introduction: Introduction: In mathematics, differentiation is the process of determining the…

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: If f(x, y) = (xy)", with |xy| < 1, find 2 af af and n=0 fe -y/(1-xy)^2 af -x/(1-xy)^2 dy

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Q: Evaluate SS 5ex+y+" dV over B where B = {(x, y, z) : x² + + z² < 1}. Take = 3.

A: The integrals in the form ∭f(x,y,z)dV is called a triple integral. In this problem, we have to…

Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: (d) VX € P(N), XCR. (e) In ɛ N, VX e P(N), |X| < n. (f) Vn e Z, 3X c N, |X| = n. (g) 3me Z, Vn € Z,…

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Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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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: If z = xe, æe then dz = (e )dx + (ryev" )dy. Select one: OTrue OFalse

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Q: E=D{(r,0,2): 0s es n, Os zs 1, Vzs rs 1.

A: Given,          E=r, θ, z : 0≤θ≤π, 0≤z≤1, z≤r≤1 To find:           ∫∫∫Ey2ex2+y23dV

Q: 1. Evaluate ff. y dS where S is the portion of the cylinder 4x2 + 2y2 = 16 that lies between z = 0…

A: Since you have asked for a question with multiple sub-parts, we will solve the first question for…

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: S[(vxvø)•nds, The value of where o(x, y, z) is defined on S is (a) 1. (b) 0. (c) 2x.

A: Concept:

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: (b) [[[ yzcos(x* }HV where E = {(x, y, z) |0 < x <1, 0 < y s.x, x S z < 2x } E

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Q: 1. If x, y, z E R, prove that (c) ||x| – |y|| < |x –yl. (d) \xy| < }(x² + y²)

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Q: Find the values of x, y and z using Gauss Jordan method. 3x +4y +z = 10 2x – 3y+ 5z +9=0 * +2y – z =…

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Q: (4) Evaluate : S[(xy? + yz') dV if Q = {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 21}

A: Note: As per our company guidelines we are supposed to answer only one question at a time. Kindly…

Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

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Q: If T = x' - xy+ y', x = pcos 4, y = psin ø %3D Find a) - ôp ƏT b)

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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: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x

Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

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Q: 3) f(x, y, z) Зху %3D z- Vx

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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: In general, E(XY) + E(X) × E(Y), but if X and Y are E(XY) = E(X) × E(Y). independent RVs,

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Q: Given dy/dx = x²+y² and y(1) = 1.5, y(1.2) = 1.704, y(1.4) = 1.911, y(1.6) = 2.213, evaluate y(1.8)…

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Q: 3. If PY = 3, YZ =5 and PV = 12, find WV. 4. If PW = YZ = 5 and PY = 10, find PV %3D %3D Z. 23

A: Topic:- secant secant method in circles

Q: Find the most general antiderivative. 4) (15+ e2t) dt. 16 e2t A) B)+ 202t + C e3t +C +C 27 e2t +C

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Q: (b) Compute f er+uds, where c(t) = (t, 2t), t e [1, 2]. %3D

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

A: We have to evaluate given integral:

Q: Find the most general antiderivative. 3 31 OA, 4. 4 3x 4. 1 +C 7x 1 O B. +. + C 4x 4 2, 49 4 -1 OC.…

A: let's find antiderivative of given function.