16. f(x, y, 2) = y - Vr? + z?; P(-3, 1, 4); a 2i-2j-k

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

A:

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: 5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz(…

A: Chain rule of partial derivatives: Let us consider a two variable function  z=f(x,y)  where ,…

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

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: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

A:

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

A:

Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

A:

Q: 2x-y if F(x, y) = xy é e af ар ay ах find

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 14. Find the distance between the two skew lines. x = 2+t x = 4+s y = 3-t y=1+s z = 4t z = 2- 2s

A: Given query is to find the the distance between two skew lines.

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: 37. f(x,y) = 9-x² – 7y³; f.(3, 1), fy(3, 1)

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 6) If F = (3x²y – z)i+ xz3 + y*)j – 2x³z²k, find V(V - F) at the point (2,1,0).

A:

Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

A:

Q: Show that fdx + gdy = S 36x°y?dx + 18yx*dy is independent of path: (3,6) (-2,4) (3,6) 2,4) C(3,6)…

A: The vector field is conservative if the components satisfy the test ∂P∂x=∂Q∂x. If the field is…

Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

A:

Q: If FGx) = -2x+s firid f(z)

A: Given: if f(x)=-2x+54To find: f(1)

Q: Find ƒxx ( x, y)  and ƒxy( x, y).

A: Given, fx,y=3x+yx-1. The objective is to find fxxx,y and fxyx,y.   fxxx,y is found as follows: First…

Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: s for :   (x,y)-->(1.5x,1.5y)

A: The given transformation is x,y→ 1.5x,1.5y

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

A:

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

A:

Q: f (z,y, z) = x² + y² + 2² subject to zyz = 4

A: Given: fx,y,z=x2+y2+z2 subject to xyz=4 Let gx,y,z=xyz-4 Using Lagrange Multiplier fx=λgx, fy=λgy,…

Q: f(x, y, z) = 3x + 2y + 4z, x2 + 2y2 + 6z2 = 21

A:

Q: 9. If y = V-|x|, then Dr = %3D %3D

A: Df :  Domain of function f  The set of all input values where f defined

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

A:

Q: Find fy(x,y) and fy(x,y). Then, find fy(- 3,1) and fy(1, – 4). f(x,y) = In |7 + 4x°y²|

A: Let f(x,y) be the given function .Then fx is the derivative of f with respect to x  , treating y as…

Q: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (

A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)

Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

A:

Q: 8.xy² If u = and error in x, y, z be 0.001, compute the maximum absolute and relative z³ error, when…

A: Given equation be u=8xy2z3 error in x, y, z be 0.001 Now ∂u∂x=8y2z3, ∂u∂y=16xyz3, ∂u∂z=-24xy2z4  and…

Q: The antiderivative of the function 4 .3 + 10x³ is, 4 f(x) - -4 .3 + 2.5x³ + c 4 -10 + 1.0xª + c -4 +…

A: According to question given f(x)=44.3+10x3We have to calculate the antiderivative

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).

A:

Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

A: We have to find grad(divV ) at (2,-1,0) where  V = (3x2y-z,xz3+y4,-2x3z2)

Q: f (x, y) = {* - kx(x — у),0 <x< 2,-х <у<х elsewhere

A: (i) Consider the property for a joint PDF, ∫-∞∞∫-∞∞fx,ydydx=1 Substitute the values,…

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

A:

Q: 2. 2sin(хy) at x D 2, у3D Зя/4 3. z= In(x + 1) + y° at the point (0,3,9)

A:

Q: e-", if 0 3,

A:

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

A:

Q: (b) ƒ(x, y) = Vy – x · In (y+x) -

A: Given (b) f(x,y)=y-x ln (y+x)

Q: O, x = 2, y = dy dz is

A:

Q: Suppose that z = f(x,y), find for 4 x²z* – 5yz³ + xy? - 3z? = x

A: Given: 4x2z4−5yz3+xy2−3z2=xz=f(x,y)∂z∂x=?

Q: At what interval is y=2r4- 4x2 concave upward? U x> 3 x 3 3 <x<- 3 3

A: The given function is y=2 x4-4 x2 We have to find the interval at which the function is concave…

Q: Is F(x,y)= (2²y,5– zy²) source free?

A:

Q: 3. r/s*t/u- v + w * x - y++

A: Given expression is, rs*tu-v+w*x-y++

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

A:

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A:

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

A:

Q: f(L,K) + x [loo-PeL-Pak] max dQ

A:

Q: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.