GIVEN S(x, y) = {0. , 0

Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

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: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: 2 Exercise.8 Find: P4 (x), Pg(x), L P¾(x) P3(x) dx , LIP,(x)|² dx

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Q: If the joint p.m.f. of X and Y is given byh(x , y) = k(x+ y)2, x = -1, 0, 1 and y = 0, 2, 4.where k…

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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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: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

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Q: s for :   (x,y)-->(1.5x,1.5y)

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

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

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

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Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: 1. For U, iid uniform on (-0,0) show that - min, {U,} is sufficient for e > 0.

A: # given ui follow  uniform distribution (-theta,0) then to show that -min(ui) be the sufficient…

Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: Given f(x,y,z)=√(−6x+5y+2z), find fx(x,y,z) = fy(x,y,z) = fz(x,y,z)=

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Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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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

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Q: (1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

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Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

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Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

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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: Given f(æ, y, z) = 6x² + 3y² + 4z², find f-(x, y, z) = | fy(x, y, 2) = | f:(x, y, z) =

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Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

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

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Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

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Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

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Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

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Q: Find y' if y= In coshv tanh v. y =sech v-2tanh v O None of the above O Option 4 y=tanh'y y'=tanhv –…

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Q: 7) If z(x,y) = x² + y², x=u+v, and y=u-v, find dz du

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Q: See image below.

A: Given that the tangent line touches the curve y = f(x) at (4, 3) passes through the point (0, 2).…

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.