1. Let A = {a, b, c}, B = {1,2,3}, C = {x, y, z, w}, D = {4,5, 6}. Let the functions f : A → B, g : B → C, h : C → D be defined by: f = {(a, 2), (b, 1), (c, 2)} g = {(1, y), (2, x), (3, w)} h = {(x, 4), (y, 6), (z, 4), (w, 5)}. Determine if each function is: (a) Onto (b) One-to-One

Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

Q: Let Ms, 0 = Rus, (), Ms. 0), where F, u, and v are differentiable, and the following applies. u(6,…

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Q: Answer with True or False. 1. The functions from Z to Z is onto if f(n)=n−1. 2. These function…

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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 f X,Y (x, y) = (x+y)/21…

A: The given joint pmf of X and Y can be described as X.       Y 1 2 P(X = x) 1 2/21 3/21 5/21 2…

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: 10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b,c, d}, Tx = {0, X, {a},…

A: Definition: A function f is continuous from X to Y if inverse image of each open set in Y is open in…

Q: If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y,…

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Q: Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b,c, d}, Tx = {6, X, {a}, {a,…

A: We use the definition of continuous map

Q: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows: R = {(0, 1), (1,1), (2,…

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Q: (a) Express du / ax, du/ ay, and du / az as functions of x, y, and z both by using the chain rule…

A: Solving

Q: 1. Let f(x,y, z) = vx + /y- Vz +In(49 – x² – y² – z²). Evaluate f(4, 4, 4).

A: Substitute the values

Q: Let W(s,t) F(u(s, t), v(s, t)) where u(1,0)-4, u,(1,0) 3, u(1,0)- 5 v(1,0) 7, v.(1,0)=-3, v(1,0)--6…

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Q: Find fy, fy, and f, and evaluate each at the given point. ху fx, у, 2) (8, 1, –1) x + y + z f,(x, y,…

A: We know that the division rule of partial derivative , If f ( x , y , z ) = h ( x , y , z ) / g ( x…

Q: Suppose z = z(x,y) is x + y+z = e¬(x+y+z) , then which relation is correct? az D): az az az az 1 ду…

A: The solution is given as follows :

Q: Let (w, x, y, z) = wxy + x² tan z and a = (1, -2,3,4). Then w(a): .₂(a) = -6 -2 8 60 -8 1-1 2 , (a)…

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Q: 10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = (a, b,c, d}, Tx = (o, X, (a},…

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Q: Find f, and f, and evaluate each at the given point. y' f(x, y) = e*y2, (In 4, 2) f,(x, y) = %3!…

A: We can find the answer as below,.

Q: 1. Let X = {r1, X2, X3, L4} and let b : X × X → [0, 0) be symmetric with %3D b(x1,x2) = 3, b(r2, 13)…

A: As per bartleby by rules for more then 1 question only first is to be answered please upload the…

Q: Find f f, and f,, and evaluate each at the given point. ху f(x, y, z) = (2, 1, –1) %3D x + y + z…

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Q: Find fxTy and f,, and evaluate each at the given point. (x, y, z) = x2y3 + 2xyz- 4yz, (-2, 1, 2) %3D…

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Q: 9. Let X = {r1,12, 23, T4}, Y = {yı,y2, Y3}, and Z = {zı, z2}, Let R be the relation from X to Z…

A: Given: 9) X=x1, x2, x3, x4, Y=y1, y2, y3 and Z=z1, z2, z3. R=x1, z1, x2, z2, x3, z1, x3, z2 and…

Q: Let R be a relation from A={−1,0,1,2} to B={a,n,i} such that (x,y) provided that x is non-negative…

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Q: Let f : [0, 1]→R be defined by f(x) :=x3 and let P :={0, 0.1, 0.4, 1}. Compute L(P, f) and U(P, f).

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Q: Let z =f (x,y),x=x(u,v), and y=y(u,v) With x (5,3) =4 and y (5,3) =2. Calculate Z (u,v) at u=5,v=3…

A: Given- Let z = fx, y, x = xu, v and y = yu, v with x5, 3 = 4 and y5, 3 = 2.  To find- Calculate zuu,…

Q: 5. If (x, y) → (x+3,y-7)maps TUVWto TU'v'W', what is the algebraic description that will map…

A: As per rules we will solve only first question: 5. Given that (x,y)→(x+3,y-7) maps TUVW to T'U'V'W'…

Q: Let W(s, t) = F(u(s,t), v(s, t)) where F, u and v are differentiable and u(2,0) = 4 v(2, 0) = 1…

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Q: 1- Let X1, X2, X3 have the joint pdf given by 1 eita) ,-c∞ < x1,X2,X3 < ∞ -00 f(x1,X2 ,X3 ) = {…

A: Normal Distribution: A continuous random variable Z is said to follow Standard Normal distribution…

Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

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Q: Let z = f(st – 3, s? +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find f, fy, and f, and evaluate each at the given point. ху f(x, у, 2) 3D (6, 1, -1) x + y + z fa(x,…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the %3D following…

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Q: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows: %3D R = {(0, 1), (1,1), (2,…

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Q: In Exercises 61–64, find an equation for the level surface of the function through the given point.

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 10. Let (X, Tx) and (Y, Tr) be two topological spaces, such that X = {a, b,c, d}, Tx = {ó, X, {a},…

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Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y– z, z – x, x – y), then div(curlG (x, y,…

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Q: Find fy and f, and evaluate each at the given point. (x, y, 2) = x²y³ + 2xyz – 6yz, (-2, 1, 2) ,(X,…

A: Given :- f(x, y, z) = x2 y3 +2xyz-6yz  To find:- fx(x, y, z) fy(x, y,z)  fz (x, y, z)  fx(-2,1,2)…

Q: f., f, and f_, and evaluate each at the given point. x'y ху f(x, у, 2) 3- (4, 1, –1) x + y + z fx(X,…

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Q: Evaluate F dr where F(x, y, z)= (x', y’, xyz) and C is the line segment from х, у, со (1, 4, 3).

A: Use parametric to solve

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: Determine the absolute maximum and minimum values ​​of the function f (x, y, z) = (x − 3) 2 + (y −…

A: Given: f(x,y,z)=(x-3)2+(y-1)2+(z+1)2 and the set is E=(x,y,z)∈R3|x2+y2+z2=4 Consider,…

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: Let W (s, t) = F(u(s, t), v(s, t)) where W,(1,0) WŁ(1,0) = u(1,0) = -1, u,(1, 0) = −5, ut(1,0) = -7…

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Q: Find F, and f, and evaluate each at the given point. fx, y, z) - xy + 2xyz - Syz, (-2, 1, 2) ,G Y.…

A: topic - partial differentiation

Q: Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b, c, d}, Tx = {ø, X, {a}, {a,…

A: We need to check the necessary and sufficient conditions for continuity

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Find f and f, and evaluate each at the given point. y' f(x, y) = e*y, (In 4, 2) f,(x, y) = f,x, y) =…

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Q: Let f(x, y, z) = 2x(y+z), x uv, y = v w, and z = w. Find in terms of u, v, and uw.

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