Let u (E) =0, then u (EUF) = (F) VFCR. %3D

Q: (d) UV, = i = 1 (e) %3D i = 1 (f) U V, = i = 1 (g) 00 i = 1

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

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Q: Let f (x, y) = 3x2 + 2xy + 5y. (a) Calculate df/dx (1, 4). (b) Evaluate df/dy at (x, y) = (1, 4).

A: Differentiate the function f with respect to x treating y as a constant to calculate ∂f∂x.

Q: ху f(x,y,z) =- х+у+z

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Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

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Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y & z considering other as constant at…

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: Evaluate e |/| 2xz dV where E = {(x, y, z) | 0 < z < 1, ¤ < y < 2x, 0 < z < z + 3y} E Round your…

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Q: dt t In yt

A: Intregate

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

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Q: Show that E [x(t)] = 0. %3D

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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: dx The evaluation of S is Vx+1 -Vx 3

A: First we have to do rationalisation of the given expression.

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

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

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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: Where a is a constant, then a is equal to:

A: Since, the joint probability distribution function is given .. Here, wa want to the value of 'a'

Q: Let z=e"In(xy), determine dx

A: Solving the problem by doing partial differentiation.

Q: (h) Ã(x, y, z) = yɛ, – xë, (i) Ã(x, y, z) = ex + ey x² + y?

A: For the conversion between cylindrical and Cartesian coordinates,  the z-coordinate is the same in…

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

A: Given,

Q: E(x)三ㄧ-rx.VY.tmdt. Į nd Eicx) Let

A: Since f(t)=sqrt (4-t^2) is even function , so we use the property of definite integral shown on…

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: f({x, y))) for all c e R and all (x, y) E R?

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

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Q: S dy S f(x, y)dx

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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: Exl. suppose the pdf of r.v. X is [x/8, 0<x<4 fx(x)= {*/8, 0<r<4 . Find the pdf of Y =-2X +8. 0,…

A: Y= - 2X + 8, we have dydx= - 2⇔ dx =-dy2and 0&lt;x&lt;4 ⇔ -8&lt;-2x&lt;0 ⇔0&lt;-2x+8&lt;8⇔…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyz

A: Given fx,y,z=e-xyz Partial derivative means differentiating with respect to one variable keeoing…

Q: O Let f : A - B be an injection, and X, Y CA. Show that f(Xn Y) = f(X)nf(Y). |

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Q: Find dv ifv = t- dt

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Q: g(x, y, z)

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Q: dx find . diven that x>0, using the substitution u =

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Q: fy = e*, y = 1 - e-x, and x = 0 ab- %3D

A: Given: - The curves of, y=e-x, y=1-e-x and x=0 about y=4.5 To find: - The volume of a solid is…

Q: dy B] If y = e" In(u) and u = V1-x2, Find dx

A: To find

Q: e function f m (0,0) to

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Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

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: I| f(x, y, z) dV, E = {(x,y, z) | 0< x< v2, x < y < V4 – x², 0 < z < x² + y² + 8} %3D E

A: Question 3. Given integral is ∫∫∫Efx,y,zdV, E=x,y,z/0≤x≤2,x≤y≤4-x2,0≤z≤x2+y2+8 It has to find the…

Q: f(x, y) = e&z– 4y af af ду

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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: 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: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

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Q: e of the function g(x y, z) = 1/xz + e%.

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Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: dy If y = e" In(u) and u = V1-x2, Find dx

A: y = eu ln(u)       and   u = 1-x2 dydx = ?