o Show that X2 = {(x, y) E X x X : x

Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: Which of the following is homogenous of smallest degree? (A x+y B) In x - In y x4+y4 x-y D Vx-y

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Q: Which of the following is homogenous of smallest degree? x-y (A x-y В Inx - In y Vx+y x4+y4 D X

A:

Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 2. Show that 4=x i+y°j+:'k is irotational.

A:

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

A:

Q: Show that the Cobb-Douglas production function z = Cxay1−a can be rewritten as        ln z/y = ln C…

A: Given: z=cxay1-a for converting given function in log we simplify it and then take log both side so,…

Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: Let p(x)= e5x be the standard integrating 3 factor to x y' +p(x)y =x°. Find p(8).

A: We have to find the value of p(8).

Q: 2. If A = f+ g,+ hy s.t f(x.y.z) = e2x, g(x.y.z) = xcosy, h(x. y. z) = log 2z then div A %3D %3D

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Q: Let f(x, y, z) = In(x² + z) + y²e®%. Find fzym. Zyx•

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Q: If the Wronskian of the DE x’y' + xp(x)y' + 3y = 0 is μ (x) er Find p(x) = %3D

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Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: Use the linear approximation (1 + x)k = 1+ kx, as specified. Estimate 1.012.

A:

Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: 2. A firm produces two goods in pure ompetition &amp; has the pllowing TR &amp; TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

A:

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: Find the particular antiderivative that satisfies the following conditions: C' (x) = 2x² – 4x; C(0)=…

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Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: The ops y' =esx-7Y;s Separable

A:

Q: Suppose there is no known formula for g(x), but we know that g(2) = -1 and d (z) = V2 +5 for all x.…

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Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: Slp xeydydx R= {(xy)|(0<x<1),(0<ySx²)}; R = limits %3D а. 2е + 1 b. ;-1 e 2 С. e + 2 d. None of the…

A: We have to evaluate integral.

Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

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Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: Given the data below about the Axial Strain(%) vs Deviator Stress: Axial Strain (%), x 2 Deviator…

A: We can solve this by using given information 0 0 1 27.227 2 44.92 3 59.776

Q: suppose the cdf of r.v. X is given by 1- e -2 x x > 0 F(x) = x < 0 Please find its pdf, and compute…

A: It was stated to suppose that X is a random variable. The given CDF is as follows:  Fx=1-e-2x ;…

Q: Consider the S.mpto lincar rogressic 3:0n m adol Y tX; t U ukon exp(az.) You have the fallow. ng…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: If z = e4x + y In(x), find zx and zy. Zx Zy %3D

A: 1) The given function is: z=e4x+ ln(x)

Q: by

A:

Q: 4.18 Given that g(x) > 0 has the property that 6. show that is a pdf. f(x, y) 2g g(x) dx = 1, (√x² +…

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Q: Find the Wronskian of a given set {yı, y2} of solutions of 6. y"3(x21)y- 2y 0, given that W(T) = 0.

A: Given the differential equation and the value of the wronskian at pi as:

Q: x'y=x'+ xy. linear DE Which value of k, the given DE will be homogenous?

A:

Q: 1 3. Integrate the function f (x, y) = over the region bounded by x-axis, line x = 7, and the curve…

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Q: {x} € 1, Show that property (3) of a matroid implies: For any S e there exists y € S, such that S \…

A: Following is the definition of a matroid. A finite matroid M is a pair (E,?), where E is a finite…

Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: QUESTION 1 Compute [[ ev** where Q is bounded by y = V100-x-z AP 2++ and y = 0.

A:

Q: Consider the following blending problem, where the gredient x3 is a semi-continuous variable: min…

A:

Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: Show (in terms of e - 6) that a function f : R → R defined by f(r, y, 2) = (2x + 3y + 42) is…

A:

Q: 2- Calculate the part a) using the given countour and assuming that R → o. For part b), e 3ix use…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

A:

Q: Find the linearization L(x) of y = e6« ln(x) at a = 1. L(x) =

A: